PickSmartly Review

Best Differential Geometry in 2026

9.9 PM Score
Products Evaluated
3
Reviews Analyzed
29
Brands Ranked
3
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Differential geometry is the sophisticated intersection of multivariable calculus and topology, providing the mathematical language necessary to describe curved spaces, manifolds, and the very fabric of general relativity. Unlike standard Euclidean geometry, which deals with flat planes and straight lines, differential geometry requires a deep dive into how local properties change as one moves across a surface. Whether you are a graduate student embarking on a research path, a theoretical physicist modeling spacetime, or a computer scientist working on non-Euclidean machine learning, selecting the right foundational text or computational tool is a decision that will dictate the trajectory of your learning curve.

Editor's Choice

Our Top Picks for Differential Geometry

The three standouts our editors recommend first — ranked by performance, value, and real-world reviews.

Mastering Essential Math Skills, Book 1: Grades 4 and 5, 3rd Edition: 20 minutes a day to success (Stepping Stones to Proficiency in Algebra)

Math Essentials Mastering Essential Math Skills Book 1

4.6 (1,407 ratings)
MATH ESSENTIALS 8.50 X 0.40 X 11.00 Inches 0.93 Pounds

Reviews for MATH ESSENTIALS (PM Score)

9.8 PM Score
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Amazon.com 9.68 Yes Yes Yes

A Tuesday afternoon kitchen table becomes much less stressful when your fourth or fifth grader can tackle math problems in just twenty minutes. Mastering Essential Math Skills, Book 1, is designed specifically to bridge the gap between basic arithmetic and the foundational logic required for algebra. Rather than overwhelming students with marathon study sessions, this third edition focuses on short, impactful bursts of learning that fit easily into a busy family schedule. It acts as a crucial stepping stone for proficiency, helping students build the confidence they need to handle more complex mathematical concepts without the typical burnout. It is a practical tool for parents looking to bolster math fluency through consistent, manageable daily practice.

What We Like
Twenty-minute daily sessions
Algebra proficiency foundation
Grades four and five
Third edition update
Essential skill building

Math Refresher for Adults: The Perfect Solution (Mastering Essential Math Skills)

Math Essentials Math Refresher for Adults

4.5 (1,411 ratings)
MATH ESSENTIALS 8.50 X 0.61 X 11.00 Inches 1.40 Pounds

Reviews for MATH ESSENTIALS (PM Score)

9.7 PM Score
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Amazon.com 9.68 Yes Yes Yes

Does the sudden sight of a complex equation make your heart race with unnecessary anxiety? Math Essentials has crafted a specialized resource designed specifically to bridge the gap for adult learners who feel they have lost their mathematical footing over the years. This book serves as a dedicated toolkit for mastering essential skills without the condescending tone often found in academic textbooks. Instead of overwhelming you with dense theory, it focuses on practical application and refreshing the foundational concepts you actually need for daily life or professional advancement. It is a refreshing, low-stress approach to reclaiming your confidence in a subject that many of us have spent years avoiding.

What We Like
Essential skill mastery
Adult-focused learning
Foundational math concepts
Confidence building

No-Nonsense Quantum Field Theory: A Student-Friendly Introduction

No-Nonsense Quantum Field Theory Student Introduction

4.6 (217 ratings)
NO-NONSENSE BOOKS 9783948763015 7.44 X 1.45 X 9.69 Inches 2.50 Pounds
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

Why does the most complex subject in modern physics often feel like it is written in a language only a handful of people can speak? No-Nonsense Quantum Field Theory: A Student-Friendly Introduction aims to dismantle that barrier by providing a clear, accessible entry point for learners. Instead of getting lost in impenetrable mathematical jargon or overly dense academic prose, this book focuses on making the core concepts digestible. It serves as a vital bridge for students who are ready to tackle the complexities of field theory but need a guide that prioritizes clarity and intuition. It positions itself as an essential toolkit for anyone serious about mastering the fundamental building blocks of our universe without the typical pedagogical headaches.

What We Like
Student-friendly approach
Clear theoretical introduction
Accessible physics concepts
No-nonsense methodology

Engineers' Practical Databook: A Technical Reference Guide for Students and Professionals

Engineers' Practical Databook Technical Reference Guide

4.6 (742 ratings)
6.00 X 0.38 X 9.00 Inches

Reviews for (PM Score)

9.6 PM Score
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Amazon.com 9.68 Yes Yes Yes

Engineers' Practical Databook is an indispensable technical companion that distills complex data into a portable, high-utility format. Whether you are a student navigating rigorous coursework or a working professional in the field, having a reliable reference at your fingertips changes how you approach problem-solving. This guide functions as a mental shortcut, providing the essential formulas and constants required to move through calculations without constant digital searching. At its current price point, it offers significant value for anyone needing a physical anchor for technical information. It is the kind of resource that belongs in a toolkit or a backpack, serving as a bridge between theoretical classroom concepts and real-world application.

What We Like
Technical reference guide
Essential engineering data
Student friendly
Professional utility
Portable format

General Relativity: The Theoretical Minimum

General Relativity: The Theoretical Minimum Physics Guide

4.6 (114 ratings)
5.85 X 1.55 X 8.85 Inches 1.10 Pounds

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9.6 PM Score
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Amazon.com 9.68 Yes Yes Yes

You might assume a book on general relativity is destined to be an impenetrable wall of math that leaves you feeling more confused than when you started. However, General Relativity: The Theoretical Minimum manages to bridge that gap by offering a structured, logical approach to one of the universe's most complex subjects. While it doesn't shy away from the necessary physics, it serves as a vital roadmap for anyone serious about moving past pop-science metaphors and into actual theoretical understanding. At a price point, it acts as an accessible entry point for students or curious intellectuals who want to grasp the mechanics of spacetime without getting lost in unnecessary fluff. It is a focused, essential addition to any science enthusiast's library.

What We Like
Theoretical physics guide
Spacetime mechanics focus
Structured learning approach
In stock now

The Age of AI: And Our Human Future

The Age of AI: And Our Human Future

5.50 X 0.85 X 8.25 Inches 0.57 Pounds

Reviews for (PM Score)

9.5 PM Score
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SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

The Age of AI: And Our Human Future takes on the question most of us keep pushing to the back of our minds: what happens to human society as intelligent machines take over more of the thinking? Instead of drowning readers in technical jargon, it steps back and examines the bigger picture — how AI shapes decisions, power, and the way we understand ourselves. It rewards slow reading, with arguments that build across chapters and plenty of moments where you'll want to argue back. In stock and easy to pick up, this is a smart choice for anyone trying to make sense of a fast-moving subject without needing a computer science degree.

What We Like
Big-picture AI thinking
Human future focus
Societal impact questions
Accessible, non-technical tone
Prompts real discussion

Essential Math for Data Science: Take Control of Your Data with Fundamental Linear Algebra, Probability, and Statistics

Essential Math for Data Science Guide

4.5 (134 ratings)
7.00 X 0.75 X 9.00 Inches 1.23 Pounds

Reviews for (PM Score)

9.5 PM Score
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HAIRDAZZLE 5.37 Yes Yes Yes

Essential Math for Data Science serves as a foundational roadmap for anyone looking to master the mathematical backbone of modern analytics. This book cuts through the noise by focusing specifically on the three pillars required for technical fluency: linear algebra, probability, and statistics. Instead of getting lost in abstract theory, it provides the practical clarity needed to actually control and interpret complex datasets. It feels like a highly accessible investment for students or career switchers who need to bridge the gap between basic coding and advanced data modeling. It is a straightforward, no-nonsense resource that turns daunting mathematical concepts into actionable knowledge for the aspiring data scientist.

What We Like
Linear algebra focus
Probability fundamentals
Statistical mastery
Data science foundation

Tutor in a Book's Geometry

Tutor in a Book Geometry Study Guide

4.4 (547 ratings)
TUTOR IN A BOOK BLACK & WHITE ILLUSTRATIONS 8.50 X 0.67 X 11.00 Inches 1.52 Pounds

Reviews for TUTOR IN A BOOK (PM Score)

9.4 PM Score
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  • Used Book in Good Condition
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

The crisp, slightly matte texture of the pages tells you immediately that this is a well-maintained resource ready for heavy study sessions. Tutor in a Book's Geometry serves as a practical companion for anyone tackling the complexities of shapes, angles, and spatial reasoning. Since this specific copy is a used book in good condition, you get the benefit of a proven educational tool without the premium price tag of a brand-new textbook. It feels substantial in your hands, making it a reliable desk staple for late-night math drills or classroom prep. At just under thirty dollars, it hits that sweet spot for students looking for effective, accessible instructional material that doesn't feel worn out.

What We Like
Good used condition
Geometry study resource
Practical math guide
Affordable educational tool

Geometry Proofs Essential Practice Problems Workbook with Full Solutions

Zishka Publishing Geometry Proofs Practice Workbook

4.4 (272 ratings)
ZISHKA PUBLISHING 8.00 X 0.47 X 10.00 Inches 0.93 Pounds
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

After weeks of use, the clarity provided by this Zishka Publishing workbook has become a staple in my daily study routine. Geometry proofs are notoriously difficult for most students, but this collection of essential practice problems breaks down complex logic into manageable steps. What sets this resource apart is the inclusion of full solutions, which allows you to immediately verify your reasoning rather than getting stuck in a loop of uncertainty. It serves as a practical bridge between reading theory and actually applying it to rigorous mathematical proofs. At a very accessible price point, it is a straightforward, no-nonsense tool for anyone looking to sharpen their geometric reasoning skills without unnecessary fluff.

What We Like
Essential practice problems
Full solutions included
Logical proof training
Geometry skill builder
#17

Differential Geometry Of Curves And Surfaces (Undergraduate Texts In Mathematics)

SPRINGER 44982825 6.27 X 0.99 X 9.52 Inches 16.63 Pounds

Reviews for SPRINGER (PM Score)

7.0 PM Score
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Books & Bauble 9.93 Yes Yes Yes

Friendly Approach To Functional Analysis, A (Essential Textbooks in Mathematics)

A Friendly Approach to Functional Analysis Textbook

WORLD SCIENTIFIC PUBLISHING EUROPE LTD 6.00 X 0.93 X 9.00 Inches 1.15 Pounds
  • Friendly Approach To Functional Analysis, A
  • World Scientific Publishing Europe Ltd
  • ABIS BOOK
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

Staring at a dense, impenetrable wall of abstract mathematical proofs can turn even the most dedicated student into a frustrated skeptic. This textbook from World Scientific Publishing Europe Ltd changes that dynamic by reframing complex functional analysis through a more accessible lens. Rather than drowning the reader in pure abstraction without context, the text prioritizes a pedagogical style that feels intuitive and supportive. It functions as an essential companion for anyone navigating advanced mathematical theory who needs a bridge between rigid formalism and actual comprehension. The approach is clearly designed to lower the barrier to entry for high-level concepts, making it a reliable resource for serious study sessions or academic deep dives.

What We Like
Accessible mathematical theory
Pedagogical approach
Essential academic text
Clear functional analysis
#21

300 Problems In Special And General Relativity

41290335 6.69 X 0.83 X 9.61 Inches 1.41 Pounds

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5.7 PM Score
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Amazon.com 9.68 Yes Yes Yes

Collected Papers On Wave Mechanics

Collected Papers On Wave Mechanics

6.00 X 0.77 X 9.00 Inches

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5.6 PM Score
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Amazon.com 9.68 Yes Yes Yes

The dense, intellectual weight of this volume hits you the moment you hold it, signaling a deep dive into the foundations of quantum theory. Collected Papers On Wave Mechanics serves as a cornerstone for anyone serious about studying the historical and mathematical evolution of physics. Rather than a modern textbook, this collection offers a direct window into the seminal thoughts that shaped our understanding of the subatomic world. It is a specialized resource that demands focus, but for a researcher or a dedicated student, having these primary sources in one place is invaluable. At its current price point, it remains a highly accessible entry point for building a serious academic library focused on the mechanics of waves.

What We Like
Foundational physics text
Academic research resource
Seminal wave mechanics
Essential scholarly collection

The Large Scale Structure of Space-Time: 50th Anniversary Edition (Cambridge Monographs on Mathematical Physics)

The Large Scale Structure of Space-Time 50th Anniversary Edition

6.00 X 1.00 X 9.00 Inches 1.76 Pounds

Reviews for (PM Score)

5.5 PM Score
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SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

The Large Scale Structure of Space-Time: 50th Anniversary Edition is a definitive cornerstone of mathematical physics that remains essential decades after its initial release. This milestone edition preserves the rigorous intellectual depth required to navigate the complexities of gravitational theory and cosmic geometry. Reading through these pages feels like engaging with the very foundation of modern cosmology, offering a level of precision that few contemporary texts can match. Whether you are a seasoned academic or a dedicated student of theoretical physics, the clarity of the mathematical frameworks presented here is unparalleled. It is a substantial, authoritative volume that serves as both a historical landmark and a functional tool for anyone serious about understanding the architecture of our universe.

What We Like
Anniversary edition
Mathematical physics monograph
Foundational cosmic theory
Rigorous academic text
#25

Modern Differential Geometry for Physicists: Second Edition (World Scientific Lecture Notes in Physics)

Modern Differential Geometry for Physicists Second Edition

WSPC ILLUSTRATIONS 6.00 X 0.64 X 9.00 Inches 0.92 Pounds

Reviews for WSPC (PM Score)

5.5 PM Score
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  • Used Book in Good Condition
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

Modern Differential Geometry for Physicists: Second Edition serves as a rigorous cornerstone for anyone tackling advanced theoretical frameworks. This WSPC edition bridges the gap between abstract mathematical theory and practical physical application with impressive clarity. While this specific copy is a used book, it arrives in good condition, making it an accessible entry point for students or researchers looking to dive into the World Scientific Lecture Notes in Physics series. It manages to handle complex geometric concepts without losing the reader in unnecessary abstraction. If you are navigating the complexities of general relativity or field theory, having this structured guide on your desk is a genuine game-changer for your study sessions.

What We Like
Second edition
Good used condition
Physics focused
Lecture note format
#30

First Steps In Differential Geometry: Riemannian, Contact, Symplectic (Undergraduate Texts In Mathematics)

SPRINGER 29 BLACK & WHITE ILLUSTRATIONS, 25 COLOU 6.10 X 1.01 X 9.25 Inches 14.19 Pounds

Reviews for SPRINGER (PM Score)

5.2 PM Score
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SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes
Buying Guide

A Guide to Selecting the Best Differential Geometry

A Guide to Selecting the Best Differential Geometry

Determine Your Mathematical Maturity

The most critical factor in selecting a resource for differential geometry is your existing mathematical foundation. This field is notoriously heavy on abstraction and rigorous proofs. If you are coming from an undergraduate background, you should look for texts that bridge the gap between vector calculus and manifold theory. A good entry-level resource will spend significant time on the 'calculus on manifolds' aspect—specifically exterior algebra, differential forms, and the concept of a tangent space. If you jump straight into advanced Riemannian geometry without a firm grasp of smooth manifolds, you will likely find the notation impenetrable. Conversely, if you are an advanced researcher, you should prioritize texts that dive straight into curvature tensors, connection theory, and global differential geometry.

Choose Between Intrinsic and Extrinsic Approaches

Differential geometry can be approached from two distinct philosophical directions. Extrinsic geometry treats surfaces as objects embedded within a higher-dimensional Euclidean space (think of a sphere sitting inside 3D space). This is often more intuitive for beginners because it allows for visual reasoning. Intrinsic geometry, however, treats the manifold as a self-contained universe where the geometry is determined by measurements made entirely within the space itself, without reference to an outside container. For physicists and topologists, intrinsic geometry is the gold standard, as it aligns with how we understand the universe. When shopping for materials, check the table of contents to see if the focus is on embedding theorems or on the intrinsic properties of the metric tensor.

Balance Rigor with Geometric Intuition

A common pitfall in this category is selecting a book that is either 'too dry' or 'too hand-wavy.' The best resources strike a delicate balance. You want a text that provides the rigorous epsilon-delta proofs required for mathematical legitimacy, but also includes high-quality diagrams and visual representations of concepts like geodesics, sectional curvature, and parallel transport. If a resource relies solely on dense algebraic manipulation without providing a geometric 'picture' of what is happening, you may struggle to develop the intuition necessary for high-level problem solving. Look for mentions of 'visualizing manifolds' or 'geometric intuition' in the preface or reviews.

Application-Specific Requirements

Your end goal should dictate your selection. If your interest lies in General Relativity, you need a text that emphasizes Lorentzian manifolds, pseudo-Riemannian metrics, and the Einstein field equations. If you are a computer vision specialist or a geometric modeling engineer, you should look for resources focusing on discrete differential geometry, which applies these concepts to meshes and digital surfaces. The mathematical machinery used for a smooth, infinitely differentiable manifold is significantly different from the machinery used for a discrete, simplicial complex. Ensure the material aligns with your specific domain of application to avoid wasting time on irrelevant theoretical frameworks.

Ready to choose?

Jump back to our ranked picks or compare the shortlist side by side.

Frequently Asked Questions

Quick answers about Differential Geometry before you buy.

Textbooks are designed for pedagogical progression, moving from foundational manifolds to complex curvature tensors, while reference manuals serve as dense, high-level repositories of theorems and identities for active researchers.

Yes. Because differential geometry relies heavily on the concept of manifolds, a working knowledge of point-set and algebraic topology is essential to understand how local properties integrate into global structures.

A strong command of multivariable calculus, linear algebra, and vector analysis is mandatory. You must be comfortable with partial derivatives, Jacobian matrices, and inner product spaces before diving into differential forms.

Focus on the relationship between exterior algebra and integration. Understanding how forms act as integrands on manifolds is more intuitive than simply memorizing the wedge product rules.

This depends on your goal. Riemannian geometry is the standard for studying curved spaces and general relativity, whereas symplectic geometry is the foundational language of classical mechanics and Hamiltonian systems.

While many books are purely mathematical, those focused on 'Geometric Mechanics' or 'General Relativity' will assume familiarity with tensor calculus and the physical interpretation of curvature.

Yes, look for titles that emphasize numerical methods and discrete differential geometry, which are vital for computer graphics, medical imaging, and geometric modeling.

'Soft' geometry focuses on topological properties and qualitative structures, whereas 'hard' geometry involves rigorous analytical estimates, PDEs, and precise metric calculations.
Research & Insights

Our Analysis of Differential Geometry

29 Reviews Analyzed
3 Products Evaluated
3.1 Avg PM Score
3 Brands Ranked

Top 10 Differential Geometry Brands on Amazon

Share of top-ranked products by brand, from our editorial analysis.

  1. 01 Cambridge University Press 1 (33.3%)
  2. 02 Moxic 1 (33.3%)
  3. 03 Wspc 1 (33.3%)

What Our Analysis Found

We've carried out a comprehensive analysis of 29 reviews on Differential Geometry, using our selection criteria to identify the best options in the categories. Our findings reveal that most customers typically select Differential Geometry priced around $50.83.

Our team of expert editors reviewed these high-quality items and handpicked the top 30 Differential Geometry for your consideration..

We are dedicated to assisting our users in finding the right geometry Products based on their needs, saving them considerable time when choosing which Differential Geometry to buy. We take pride in the number of satisfied users we've helped through our thorough and insightful reviews.

Side by Side

Comparison Table

Compare the top 30 picks at a glance — select a column to sort.

# Product Brand PM Score Rating Where to Buy
1 An Introduction to Manifolds (Universitext) Springer 9.9 4.9 (114) Buy on Amazon
2 Math Essentials Mastering Essential Math Skills Book 1 Math Essentials 9.8 4.6 (1,407) Buy on Amazon
3 Math Essentials Math Refresher for Adults Math Essentials 9.7 4.5 (1,411) Buy on Amazon
4 No-Nonsense Quantum Field Theory Student Introduction No-Nonsense Books 9.6 4.6 (217) Buy on Amazon
5 Engineers' Practical Databook Technical Reference Guide 9.6 4.6 (742) Buy on Amazon
6 Differential Geometry (Dover Books on Mathematics) Dover Publications 9.6 4.6 (166) Buy on Amazon
7 General Relativity: The Theoretical Minimum Physics Guide 9.6 4.6 (114) Buy on Amazon
8 The Age of AI: And Our Human Future 9.5 4.2 (1,244) Buy on Amazon
9 Introduction to Differential Geometry of Space Curves and Su 9.5 4.5 (127) Buy on Amazon
10 Essential Math for Data Science Guide 9.5 4.5 (134) Buy on Amazon
11 Tutor in a Book Geometry Study Guide Tutor in a Book 9.4 4.4 (547) Buy on Amazon
12 Zishka Publishing Geometry Proofs Practice Workbook Zishka Publishing 9.4 4.4 (272) Buy on Amazon
13 Riemannian Geometry Springer 8.8 4.7 (81) Buy on Amazon
14 Principles of Tensor Calculus 8.3 4.4 (78) Buy on Amazon
15 Differential Geometry: Connections, Curvature, and Character Springer 7.8 4.9 (57) Buy on Amazon
16 Schaum's Outline of Differential Geometry (Schaum's Outline McGraw-Hill Education 7.4 4.6 (55) Buy on Amazon
17 Differential Geometry of Curves and Surfaces (Undergraduate Springer 7.0 4.7 (46) Buy on Amazon
18 Elementary Differential Geometry, Revised 2nd Edition Academic Press 6.9 4.3 (52) Buy on Amazon
19 A Friendly Approach to Functional Analysis Textbook World Scientific Publishing Europe Ltd 5.8 4.8 (20) Buy on Amazon
20 Lectures on Classical Differential Geometry: Second Edition Struik, Dirk Jan 5.8 4.1 (34) Buy on Amazon
21 300 Problems in Special and General Relativity 5.7 4.5 (24) Buy on Amazon
22 Differential Manifolds (Dover Books on Mathematics) Dover Publications 5.7 4.9 (16) Buy on Amazon
23 Collected Papers On Wave Mechanics 5.6 4.8 (15) Buy on Amazon
24 The Large Scale Structure of Space-Time 50th Anniversary Edition 5.5 5.0 (10) Buy on Amazon
25 Modern Differential Geometry for Physicists Second Edition WSPC 5.5 4.5 (19) Buy on Amazon
26 Differential Geometry of Curves and Surfaces (Springer Under Springer 5.5 5.0 (9) Buy on Amazon
27 Spacetime: Minkowski's Papers on Spacetime Physics 5.3 4.8 (10) Buy on Amazon
28 Differential Geometry in Physics University of North Carolina Wilmington William Madison Randall Library 5.3 4.6 (13) Buy on Amazon
29 A First Course in Differential Geometry: Surfaces in Euclide Cambridge University Press 5.2 4.5 (14) Buy on Amazon
30 First Steps in Differential Geometry: Riemannian, Contact, S Springer 5.2 4.5 (14) Buy on Amazon