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Abstract algebra learning recommendations

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This page provides subject-specific learning recommendations for the subject abstract algebra. See all our learning recommendations pages |

Abstract algebra is an important component of undergraduate mathematics that includes group theory, ring theory, field theory, and some advanced aspects of linear algebra (such as the Jordan canonical form and rational canonical form) that rely on some knowledge of ring theory and field theory.


Further information: abstract algebra learning benefits

  • Abstract algebra is largely useful only for people who intend to major in mathematics and do further work in a mathematics-intensive area (such as physics, some parts of computer science, and some parts of chemistry).
  • Abstract algebra provides a deeper conceptual foundation for linear algebra, which is quite useful.
  • The modes of thinking introduced in abstract algebra, particularly the ideas of isomorphism and homomorphism, can be useful for understanding logic, philosophy, and various cognitive science-based subjects. However, the specifics of algebraic structures are not relevant.

Books for learning

Our top general recommendations are recommendations that we would give people if we had to name just a few top books. Our niche recommendations are recommendations that suit learners with specific learning styles or goals. For learners who fit one of the niches, the niche recommendation would be better. Price ranges are provided to give better context to the strength of our recommendation.

Top general recommendations

Book Author ISBN and purchase links Price estimate (values may be outdated; also, international editions may be cheaper) Why we're recommending it and who we're recommending it for
A Book of Abstract Algebra (Second Edition, Dover) Charles Pinter ISBN 978-0486474175, Amazon $10-15 We recommend this book for people who are relatively new to higher mathematics and want a book focused on mastery of basic ideas and formalisms. It does not include too much information that sets a foundation for graduate work in mathematics. The book is also sufficiently cheap that you can buy it, use it, and then move on to more advanced books after extracting value from it.
Abstract Algebra (3rd Edition) David S. Dummit and Richard M. Foote ISBN 978-0471433347, Amazon $75-100 We recommend this book for people who are quite comfortable with mathematical abstraction and want to learn the subject in considerable depth, sufficient to be prepared for graduate study in mathematics.
A number of universities have moved to using Dummit and Foote for their (honors) undergraduate algebra sequences, moving away from books by Artin, Lang, and Herstein.
The comments on a Less Wrong thread (available here) about book recommendations made the case for the book over the books by Lang and Hungerford.

Niche recommendations

Book Author ISBN and purchase links Price estimate (values may be outdated; also, international editions may be cheaper) Why we're recommending it and who we're recommending it for
Visual Group Theory Nathan Carter ISBN 978-0883857571, Amazon hardcover $50-75 Focused only on group theory and uses a somewhat heterodox perspective. Ideal for people who want to get a taste of the subject in advance of studying it formally. This might include high school students who have some interest in higher mathematics but are currently not prepared or inclined to go through a formal presentation of the material.
Integers, Polynomials, and Rings: A Course in Algebra Ronald S. Irving ISBN 978-0387201726, Amazon paperback Hardcover ~$90, paperback ~$40 This is a very gentle introduction that is accessible to a high schooler who has learned second year high school algebra, and has some very pretty material.
Algebra (2nd Edition) (Featured Titles for Abstract Algebra) [Hardcover] Michael Artin ISBN 978-0132413770, Amazon hardcover $125 (new), $75 (used) Artin's book has a fair amount of coverage of the geometric intuition behind algebraic constructions, such as the role of groups in symmetry. However, it seems to be harder for people to do self-study from this book and obtain a comrephensive picture of the subject. We would advise this book to people who are reading with the help of a mentor who is willing to use the book, or people who have already studied the basic material and are now looking to delve deeper into the material from the perspective that Artin uses.
Basic Algebra and Further Algebra with Applications (book series) P. M. Cohn Basic: ISBN 978-1852335878, Amazon hardcover; Further: 978-1447111207, Amazon paperback Basic: $50-100 (depending on edition choice), Further: $50-100 (depending on edition choice) The book covers many interesting topics in interesting combinations. While we wouldn't recommending buying this as a main source of learning, it could be good to rent or check out from a library for interesting supplementary topics.

Video recommendations

It is worth keeping in mind that for higher mathematics in general and for abstract algebra in particular, books and other written media facilitate a far more complete learning experience than videos do. While videos can help you learn a few subtopics and give you a feel for the subjects, you will still probably need to do the majority of your learning from books or other written material.

  • Math Doctor Bob has some videos on abstract algebra including group theory: See here.
  • Vipul Naik made videos on some introductory topics in group theory to supplement his guided tour to group theory (the videos can be viewed along with the material in the tour).

Books for casual reading

These books might inspire you to learn abstract algebra, help make sense of what you are already learning or have learned, or just be entertaining. They are unlikely to directly teach you abstract algebra.

Book Author ISBN and purchase links Price estimate More about the book
The Symmetries of Things [Hardcover] John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss ISBN 978-1568812205, Amazon hardcover ~$50 Explores the significance of symmetry in nature.
Symmetry and the Monster Mark Ronan ISBN 978-0192807236 $10-20 The book reviews some of the mysterious connections between group theory and some algebraic objects that appear in number theory.