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Best Group Theory in 2026

9.8 PM Score
Products Evaluated
2
Reviews Analyzed
36
Brands Ranked
2
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Group theory is the mathematical study of symmetry, providing the foundational language for modern algebra, particle physics, and cryptography. Whether you are an undergraduate student encountering abstract structures for the first time or a researcher delving into Lie groups or Galois theory, selecting the right text is a high-stakes decision. Unlike general mathematics books, a group theory resource can range from highly intuitive, computational introductions to dense, axiomatic treatises that assume a mastery of set theory and topology. Choosing the wrong level of abstraction can lead to significant frustration or, conversely, a lack of the rigor required for advanced study.

Editor's Choice

Our Top Picks for Group Theory

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

The Fallacy Detective: Thirty-Eight Lessons on How to Recognize Bad Reasoning

The Fallacy Detective Logic Lessons Book

4.7 (1,700 ratings)
6.50 X 0.60 X 9.00 Inches 0.90 Pounds

Reviews for (PM Score)

9.8 PM Score
Buy on Amazon
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

Critical thinkers and curious students require The Fallacy Detective to navigate the increasingly murky waters of modern discourse. This book serves as a vital toolkit for anyone tired of being swayed by flawed arguments and deceptive rhetoric. Instead of dense, academic jargon that makes your head spin, it breaks down the mechanics of bad reasoning into thirty-eight digestible, practical lessons. I found that it transforms the way you process information, turning you from a passive listener into an active investigator of truth. It is an essential resource for sharpening your mental defenses and ensuring that your own logic remains airtight in a world full of intellectual shortcuts.

What We Like
Thirty-eight logic lessons
Recognize bad reasoning
Practical critical thinking

Group Theory in a Nutshell for Physicists (In a Nutshell, 17)

Group Theory in a Nutshell for Physicists

4.8 (96 ratings)
PRINCETON UNIVERSITY PRESS 9780691162690 7.25 X 2.00 X 10.25 Inches 3.25 Pounds
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Amazon.com 9.68 Yes Yes Yes

This Princeton University Press publication stands as a vital mathematical bridge for anyone navigating the complexities of theoretical physics. Rather than getting bogged down in purely abstract proofs, this volume focuses on the practical application of symmetry and algebraic structures that actually drive physical laws. It is a specialized tool designed to strip away the unnecessary fluff, providing a streamlined perspective that respects the reader's time and intellectual rigor. While the price point reflects its niche academic status, the clarity it brings to such a dense subject matter makes it a worthwhile investment for serious students and researchers. It manages to condense massive concepts into a manageable, coherent framework that feels both accessible and deeply authoritative.

What We Like
Physics-focused approach
Streamlined mathematical concepts
Academic rigor
Princeton University Press

Introduction to Graph Theory (Dover Books on Mathematics)

Introduction to Graph Theory by Dover Publications

4.6 (501 ratings)
DOVER PUBLICATIONS 160ILL. 5.50 X 0.50 X 8.50 Inches 0.51 Pounds
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

Introduction to Graph Theory stands as a premier foundational resource for mathematics students and enthusiasts seeking clarity without a massive price tag. Dover Publications has a reputation for making complex academic subjects accessible, and this volume delivers exactly that. It strips away the unnecessary fluff often found in modern textbooks, focusing instead on the core principles of graph theory in a way that feels both rigorous and approachable. At just over sixteen dollars, it is an incredibly efficient way to build a mathematical toolkit. Whether you are self-studying or looking for a reliable desk reference, this book provides a streamlined path through the essential structures of the field.

What We Like
Mathematical foundational text
Affordable academic resource
Clear theoretical approach
Dover Publications quality

Introduction to Topology: Third Edition (Dover Books on Mathematics)

Introduction to Topology Third Edition Dover Mathematics

4.5 (425 ratings)
DOVER PUBLICATIONS 5.44 X 0.45 X 8.41 Inches 0.62 Pounds
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Amazon.com 9.68 Yes Yes Yes

Mathematics students searching for a rigorous yet accessible entry point into spatial reasoning must secure this third edition. This Dover Publications volume serves as a cornerstone for anyone tackling the complexities of topological structures without breaking the bank. While many advanced math texts feel intimidatingly dense, this edition maintains a clarity that makes high-level concepts digestible. It is the kind of foundational resource you keep on your desk for years, referencing it whenever a geometric proof feels particularly slippery. At its current price point, it offers an incredible level of academic depth that is hard to find in modern, overpriced textbooks. It is a reliable, no-frills companion for serious study.

What We Like
Third edition text
Dover mathematics series
Academic foundational resource

A Programmer's Guide to Computer Science: A virtual degree for the self-taught developer

A Programmer's Guide to Computer Science by Jaxson Media

4.4 (300 ratings)
JAXSON MEDIA 9781951204006 6.00 X 0.43 X 9.00 Inches 0.58 Pounds

Reviews for JAXSON MEDIA (PM Score)

9.4 PM Score
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Amazon.com 9.68 Yes Yes Yes

A Programmer's Guide to Computer Science offers a structured roadmap for anyone tired of the endless, unorganized tutorial rabbit hole. This book functions as a virtual degree, specifically designed to bridge the gap between knowing how to code and actually understanding the underlying theory of computer science. Instead of just teaching syntax, it focuses on the foundational concepts that self-taught developers often miss during their journey. It is a dense, intentional resource that treats the reader like a professional, moving beyond surface-level hacks to build genuine expertise. Investment, you are essentially purchasing a curriculum that provides the academic rigor necessary to level up your engineering career without the traditional classroom overhead.

What We Like
Virtual degree curriculum
Self-taught developer focus
Foundational theory guide
Structured learning path

Art-based Group Therapy: Theory and Practice

Art-based Group Therapy: Theory and Practice

4.8 (69 ratings)
CHARLES C THOMAS PUB LTD 7.25 X 0.75 X 10.25 Inches 1.25 Pounds
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

Clinical psychologists and group facilitators looking to bridge the gap between creative expression and therapeutic intervention cannot afford to overlook this essential text. Published by Charles C Thomas Pub Ltd, this volume serves as a foundational roadmap for integrating artistic processes into a group setting. Rather than treating art as a mere distraction, the book approaches it as a core component of the healing process, blending rigorous theory with actionable practice. It is a specialized resource that provides the structural depth necessary for professionals to lead sessions that are both psychologically sound and creatively engaging. It represents a serious investment in professional development for anyone dedicated to the intersection of art and mental health.

What We Like
Theoretical framework
Practical application
Group therapy focus
Professional clinical resource

Group Theory and Chemistry (Dover Books on Chemistry)

Group Theory and Chemistry by Dover Publications

4.5 (74 ratings)
DOVER PUBLICATIONS 69ILL. 5.40 X 0.65 X 8.46 Inches 0.91 Pounds
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

The crisp, matte texture of the Dover paper immediately signals that this is a serious academic tool designed for heavy study sessions. Group Theory and Chemistry bridges the gap between abstract mathematical concepts and practical chemical applications with remarkable clarity. It is the kind of text that transforms intimidating symmetry operations into understandable, logical frameworks. While the subject matter is inherently dense, the presentation remains accessible for students looking to master molecular symmetry. At such an affordable price point, it serves as an essential cornerstone for any physical chemistry library, offering deep theoretical insights without the intimidating cost of modern, oversized textbooks.

What We Like
Mathematical chemistry focus
Affordable academic text
Symmetry theory coverage
Dover quality printing

Group Theory and Quantum Mechanics (Dover Books on Chemistry)

Group Theory and Quantum Mechanics Dover Chemistry Book

4.6 (67 ratings)
DOVER PUBLICATIONS ILLUSTRATIONS 5.56 X 0.74 X 8.46 Inches 0.81 Pounds
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

You are staring at a complex set of molecular orbitals and realize the symmetry is the only way to make sense of the math. This Dover Publications text serves as that essential bridge for students and researchers struggling to connect abstract algebraic structures with physical reality. It is a dense, focused resource that strips away the fluff to get straight to the mathematical foundations required for advanced quantum studies. While the subject matter is inherently demanding, the book provides a clear roadmap through the intersection of group theory and chemical physics. It is the kind of reliable, no-nonsense reference you want sitting on your desk during late-night study sessions or when you need to verify a specific symmetry operation quickly.

What We Like
Advanced mathematical focus
Chemistry specialty text
Dover Publications quality
Core quantum concepts

A Course on Group Theory (Dover Books on Mathematics)

A Course on Group Theory by Dover Publications

4.5 (57 ratings)
DOVER PUBLICATIONS ILLUSTRATIONS 5.50 X 0.75 X 8.50 Inches 0.75 Pounds
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

Advanced mathematics students often struggle to find rigorous yet accessible foundational texts that don't break the bank. This Dover Publications volume addresses that exact gap by providing a focused, academic deep dive into group theory without the prohibitive cost of modern specialty textbooks. It serves as a streamlined resource for anyone needing to master algebraic structures through a clear, structured pedagogical approach. While the content is dense and requires significant mental heavy lifting, the straightforward presentation makes it a reliable companion for self-study or supplemental classroom use. It is a rare find to encounter such high-level mathematical instruction at this price point, making it an essential addition to a serious mathematician's library.

What We Like
Rigorous mathematical content
Affordable academic text
Focused group theory
Structured learning approach

Schaum's Outline of Group Theory (Schaum's Outline Series)

Schaum's Outline of Group Theory by McGraw-Hill

4.5 (50 ratings)
MCGRAW-HILL EDUCATION BLACK & WHITE ILLUSTRATIONS 8.20 X 0.56 X 10.90 Inches 0.96 pounds
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

Mathematics students struggling to bridge the gap between abstract theory and practical application desperately need this specific resource in their study arsenal. Group theory can feel incredibly daunting when you are staring at dense, purely conceptual textbooks, but this guide changes the dynamic by focusing on the mechanics of the subject. It acts as a bridge, translating complex mathematical structures into digestible, actionable knowledge. While it lacks the narrative fluff of a standard textbook, that is exactly why it works for intense exam preparation or quick concept refreshes. You aren't just reading about groups. You are working through them. At a price point, it is a highly accessible tool for anyone looking to master algebraic structures without getting lost in unnecessary academic jargon.

What We Like
Targeted study aid
Concept-focused approach
Practical mathematical application
Essential exam resource
#16

Symmetry: An Introduction To Group Theory And Its Applications (Dover Books On Physics)

MCWEENY, R. ILLUSTRATIONS 5.56 X 0.58 X 8.50 Inches 0.61 Pounds

Reviews for MCWEENY, R. (PM Score)

6.6 PM Score
Buy on Amazon
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes
#19

An Introduction To Tensors And Group Theory For Physicists

BIRKHÄUSER 23 BLACK & WHITE ILLUSTRATIONS, 7 BLACK 6.14 X 0.75 X 9.21 Inches 14.72 Pounds

Reviews for BIRKHÄUSER (PM Score)

5.9 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

Reviews for (PM Score)

5.6 PM Score
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SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
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

Theory and Practice of Group Counseling (MindTap Course List)

Theory and Practice of Group Counseling MindTap Course List

8.50 X 0.75 X 10.75 Inches 2.00 Pounds

Reviews for (PM Score)

5.5 PM Score
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SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Apex_media🍏 9.87 Yes Yes Yes

Theory and Practice of Group Counseling delivers a sophisticated digital learning experience through its integrated MindTap platform. Navigating the complexities of group dynamics requires more than just a standard textbook, and this course list provides the interactive framework necessary for deep academic engagement. It serves as a comprehensive toolkit for students and practitioners looking to bridge the gap between theoretical frameworks and real-world application. The digital integration ensures that the material is not just read, but actively processed through the structured course environment. It is a solid investment for anyone serious about mastering the nuances of group therapy and counseling methodologies within a modern, tech-enabled educational setting.

What We Like
MindTap digital integration
Comprehensive course list
Interactive learning framework
Theory-to-practice focus

The Theory of Groups (Dover Books on Mathematics)

Dover Publications The Theory of Groups Mathematics Book

DOVER PUBLICATIONS 6.00 X 1.00 X 8.90 Inches 1.30 Pounds
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

After weeks of deep study sessions, I finally realized why this Dover Publications edition remains a staple for mathematics enthusiasts. The Theory of Groups offers a focused approach to algebraic structures that feels both rigorous and accessible for a dedicated learner. While many modern textbooks can feel bloated with unnecessary fluff, this volume gets straight to the core mathematical principles. It provides an incredible amount of academic value without the heavy financial burden of contemporary university texts. It is a reliable companion for anyone looking to solidify their understanding of group theory through a classic, streamlined lens.

What We Like
Rigorous mathematical theory
Streamlined academic content
Affordable mathematics text
Dover Publications quality
#28

Matrix Groups: An Introduction To Lie Group Theory

SPRINGER 7.01 X 0.78 X 9.25 inches 1.36 Pounds

Reviews for SPRINGER (PM Score)

4.8 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

An Introduction to the Theory of Groups (Dover Books on Mathematics)

An Introduction to the Theory of Groups

BLACK & WHITE ILLUSTRATIONS 5.40 X 0.30 X 8.40 Inches 0.30 Pounds

Reviews for (PM Score)

4.7 PM Score
Buy on Amazon
SELLER SELLER SCORE AMAZON FULFILLED PRIME FREE SHIPPING
Amazon.com 9.68 Yes Yes Yes

Mathematical clarity is often sacrificed for dense, impenetrable jargon, but this Dover publication prioritizes foundational understanding instead. While many textbooks on abstract algebra feel like they were written to gatekeep knowledge, this volume serves as a genuine gateway into the complexities of group theory. It strips away the unnecessary fluff that usually clutters higher-level mathematics, allowing you to focus on the core logical structures that actually matter. For the price of a standard lunch, you get a rigorous academic resource that remains accessible to serious students and self-learners alike. It is a rare find to see such deep subject matter presented with this level of economy and precision, making it a staple for any serious mathematics library.

What We Like
Foundational group theory
Academic rigor
Dover mathematics series
Accessible mathematical concepts
Buying Guide

A Guide to Selecting the Best Group Theory Texts

A Guide to Selecting the Best Group Theory Texts

Determine Your Mathematical Maturity

The most critical factor in selecting a group theory text is your current mathematical standing. If you are an undergraduate student, you should look for books that prioritize 'concrete' examples. A good introductory text will bridge the gap between familiar concepts—like the symmetries of a square or the permutations of a set—and the abstract axioms of group theory. Avoid texts that jump immediately into category theory or advanced module theory unless you have a strong foundation in linear algebra and basic proof techniques. If you are a graduate student, you require a text that emphasizes structure, homomorphisms, and the classification of finite simple groups, often with a more rigorous, formal approach.

Focus on the Balance of Examples and Proofs

A common pitfall in mathematical literature is the 'theory-heavy' trap, where a book provides elegant proofs but offers very little intuition. When evaluating a resource, look at the table of contents and sample chapters. Does the author provide a variety of examples, such as matrix groups, permutation groups, and cyclic groups? A superior guide doesn't just tell you what a subgroup is. It shows you how to find one in a real-world algebraic structure. Conversely, if you are preparing for research, you may actually prefer a text that focuses on the 'why' behind the theorems, prioritizing the logical architecture over a long list of computational exercises.

Identify the Specific Branch of Study

Group theory is not a monolith. Depending on your goals, you may need to specialize. If your interest lies in geometry or physics, look for texts that emphasize Lie Groups and continuous symmetries. If you are interested in number theory or cryptography, prioritize books that cover Galois Theory and finite fields. For those interested in computer science and coding theory, resources that focus on Computational Group Theory and algorithmic approaches to group structure will be far more valuable than purely theoretical treatises. Ensure the book's scope aligns with your intended application.

Check for Problem Sets and Solutions

Mathematics is learned through doing, not just reading. A high-quality group theory book must feature robust problem sets that range from basic verification exercises to deep, investigative challenges. Check if the book includes solutions to the odd-numbered problems or an appendix of hints. For self-study, a book without a comprehensive set of exercises is virtually useless, as you need a way to test your grasp of concepts like Lagrange's Theorem or the Sylow Theorems through active application.

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

Frequently Asked Questions

Quick answers about Group Theory before you buy.

Most introductory texts assume a solid grasp of basic set theory, functions, and logical proofs. Advanced volumes may require familiarity with linear algebra or abstract algebra concepts.

Yes, it is foundational for cryptography, coding theory, and understanding the complexity of algorithms and symmetry in computational geometry.

Introductory texts focus on definitions, subgroups, and basic isomorphisms, while advanced texts delve into representation theory, Galois theory, and Lie groups.

While self-study is possible with the right pedagogical text, many books are designed as supplements to a formal lecture series and may require external resources for complex proofs.

Look for texts that emphasize geometric interpretations, such as those focusing on symmetry groups, transformations, and visual representations of group actions.

Some specialized texts focus on applications in physics (quantum mechanics) and chemistry (molecular symmetry), but most standard reviews focus on pure mathematical theory.

Group theory is highly abstract. Mastery requires working through a significant volume of exercises to move beyond rote memorization of theorems to intuitive understanding.
Research & Insights

Our Analysis of Group Theory

36 Reviews Analyzed
2 Products Evaluated
5.6 Avg PM Score
2 Brands Ranked

Top 10 Group Theory Brands on Amazon

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

  1. 01 Brand: The Hamlyn Publishing Group 1 (50%)
  2. 02 Gryphon House 1 (50%)

What Our Analysis Found

We've carried out a comprehensive analysis of 36 reviews on Group Theory, using our selection criteria to identify the best options in the categories. Our findings reveal that most customers typically select Group Theory priced around $16.92.

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

We are dedicated to assisting our users in finding the right theory Products based on their needs, saving them considerable time when choosing which Group Theory 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 The Fallacy Detective Logic Lessons Book 9.8 4.7 (1,700) Buy on Amazon
2 Theory and Practice of Counseling and Psychotherapy, Enhance 9.8 4.6 (1,957) Buy on Amazon
3 Real Analysis: A Long-Form Mathematics Textbook (The Long-Fo Independently Published 9.7 4.7 (520) Buy on Amazon
4 Group Theory in a Nutshell for Physicists Princeton University Press 9.6 4.8 (96) Buy on Amazon
5 Introduction to Graph Theory by Dover Publications Dover Publications 9.6 4.6 (501) Buy on Amazon
6 Theory and Practice of Group Counseling Brooks / Cole 9.6 4.6 (469) Buy on Amazon
7 Introduction to Topology Third Edition Dover Mathematics Dover Publications 9.5 4.5 (425) Buy on Amazon
8 A Programmer's Guide to Computer Science by Jaxson Media Jaxson Media 9.4 4.4 (300) Buy on Amazon
9 Art-based Group Therapy: Theory and Practice Charles C Thomas Pub Ltd 8.3 4.8 (69) Buy on Amazon
10 Group Theory and Chemistry by Dover Publications Dover Publications 8.2 4.5 (74) Buy on Amazon
11 Group Theory and Quantum Mechanics Dover Chemistry Book Dover Publications 8.0 4.6 (67) Buy on Amazon
12 Naive Lie Theory (Undergraduate Texts in Mathematics) Springer 7.7 4.4 (65) Buy on Amazon
13 A Course on Group Theory by Dover Publications Dover Publications 7.4 4.5 (57) Buy on Amazon
14 Schaum's Outline of Group Theory by McGraw-Hill McGraw-Hill Education 7.0 4.5 (50) Buy on Amazon
15 The Theory of Groups and Quantum Mechanics Martino Fine Books 6.8 4.6 (43) Buy on Amazon
16 Symmetry: An Introduction to Group Theory and Its Applicatio McWeeny, R. 6.6 4.5 (42) Buy on Amazon
17 An Introduction to the Theory of Groups (Graduate Texts in M Springer 6.1 4.4 (33) Buy on Amazon
18 Galois Theory Through Exercises (Springer Undergraduate Math Springer 6.0 4.8 (24) Buy on Amazon
19 An Introduction to Tensors and Group Theory for Physicists Birkhäuser 5.9 4.5 (28) Buy on Amazon
20 Theory of Lie Groups (Dover Books on Mathematics) Dover Publications 5.8 4.7 (22) Buy on Amazon
21 Collected Papers On Wave Mechanics 5.6 4.8 (15) Buy on Amazon
22 Theory and Practice of Group Counseling MindTap Course List 5.5 4.9 (12) Buy on Amazon
23 Group Theory in Physics World Scientific Publishing Company 5.5 4.6 (17) Buy on Amazon
24 Adventures in Group Theory: Rubik's Cube, Merlin's Machine, Johns Hopkins University Press 5.4 4.5 (17) Buy on Amazon
25 Mathematical Methods for Physics: An Introduction to Group T 5.1 5.0 (1) Buy on Amazon
26 Introduction To Abstract Algebra, An: Sets, Groups, Rings, A 5.1 5.0 (1) Buy on Amazon
27 Dover Publications The Theory of Groups Mathematics Book Dover Publications 5.0 4.4 (12) Buy on Amazon
28 Matrix Groups: An Introduction to Lie Group Theory Springer 4.8 4.2 (11) Buy on Amazon
29 An Introduction to the Theory of Groups 4.7 4.1 (11) Buy on Amazon
30 Group Theory: Birdtracks, Lie's, and Exceptional Groups Princeton University Press 4.6 4.3 (5) Buy on Amazon