Mastering abstract algebra can be a bit of a tall task for students of all ages, and there are plenty of adults that could use a refresher course on the fundamentals of algebra as well.
Below we highlight some of the best books on abstract algebra you’ll find anywhere today, the kinds of books that will help explain the sometimes complex and convoluted mathematical principles and formulas in a way that makes them far more accessible and easy to leverage.
Best Books To Learn Abstract Algebra 2020
Only a handful of these books are actual textbooks, with the majority of them written by mathematicians that have a real knack for storytelling and creative descriptions. This makes these top-tier abstract algebra books a lot more “user-friendly” rather than fact and figure intensive that can weigh people down.
Abstract Algebra, 3rd Edition
This is one of the best books on abstract algebra you’ll find today, as well as one of the few textbooks that we are highlighting in this quick list.
The most current up-to-date version of this seminal work, this is widely regarded as the most complete and comprehensive entry-level textbook for abstract algebra – specifically aimed at helping new students better understand and appreciate the power of this form of mathematics.
The whole title is structured from start to finish with a year’s curriculum in mind, building upon the lesson plans in previous chapters to establish a concrete and fundamental and working knowledge of everything that abstract algebra has to offer.
A First Course in Abstract Algebra, 7th Edition
This book is considered a classic by mathematicians in the algebra world and for good reason.
This book really focuses on groups, rings and fields, and other more specialized aspects of abstract algebra that a lot of modern books and textbooks don’t really dive into – at least not in the kind of comprehensive depth that this title focuses on.
Not exactly a textbook but not exactly a “narrative”, either, this sits somewhere in the middle with very accessible language, easy to follow lesson plans and the kind of detail you’d expect from someone serious about mastering this core mathematics language.
A Book of Abstract Algebra: Second Edition
Very accessible, but at the same time heavy duty and dense, the material that you’ll find throughout this book may not be the easiest to digest – but you won’t find anything more comprehensive when it comes to the world of abstract algebra than this book.
Everything in the world of elementary abstract algebra is covered here, including a couple of intuitive approaches in regards to how to best learn entry-level abstract algebra before you go on to more complex and complicated formulas and equations.
Specifically created with undergraduate as well as junior and senior-level math students, there’s still a lot of value in this fundamental book for students that are pursuing higher levels of mathematics education and want a good refresher.
Contemporary Abstract Algebra
This book is almost exclusively intended to be used in advanced abstract algebra courses with students that are going to be doing computations and writing proofs more often than not.
The overwhelming arc of this book really highlights the value in obtaining a court introduction to the basics and fundamentals of abstract algebra before moving forward into something more contemporary, but as soon as those fundamentals have been clearly outlined it moves rapidly into more modern and contemporary applications.
You’ll find this book to be particularly useful for physicists, chemists, and computer scientists that leverage abstract algebra on a day-to-day basis and want something more in line with modern thinking in this field of algebra today.
Abstract Algebra: A Student-Friendly Approach
This is the best book on abstract algebra specifically focused on students that are having an otherwise difficult time getting their feet on the ground when it comes to the core concepts and fundamental basics of this abstract mathematical approach.
Not only does it condense things down into the simplest of language, making it far more accessible than the sometimes scientific meaning abstract algebra textbooks available on the market right now, but it also shows you how to think with mathematics in mind – something that won’t only prove useful when learning abstract algebra, but will prove to be immensely useful in all mathematic endeavors.
A First Course in Abstract Algebra
Anyone learning the basics of abstract algebra will want to consider choosing this book before they dive into any other. This as one of the most comprehensive top to bottom discussions of groups and rings, the backbone that the rest of abstract algebra is really built on top of.
The book goes a little more in-depth into other areas and components of fundamental abstract algebra, but it really knocks it out of the park when it comes to groups and rings and the value they have when mastering this subject for the first time.
Elements of Abstract Algebra
One of the more readable top-tier books focusing on abstract algebra, this is a college-level book that focuses on some of the more complex and advanced components of this mathematical structure but does so in a way that isn’t ever difficult to understand or digest.
It moves pretty rapidly into even more of the abstract components that college-level students are going to have to embrace as they develop their studies without ever abandoning fundamentals at the same time. This is what helps to make it one of the best books on abstract algebra on the market right now.
Concrete Abstract Algebra: From Numbers to Gröbner Bases
A bit of an older title, this is a detailed resource library then turns some of the more abstract components of this type of algebra into more concrete examples – outline things in a way that provides for a higher level of accessibility than titles that remain in the abstract world of this mathematic approach.
The best part of this book is that it was created over a number of years actually teaching abstract algebra, refined and reiterated until it has become one of the best books on the subject money can buy.
Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates
While the title of this book might lead you to believe that it covers only the basic and fundamentals of abstract algebra, nothing could be further from the truth.
This book is intended for serious students that want to pursue more advanced applications of abstract algebra, those in the world of physics, engineering, and computer science at the undergraduate and graduate levels. There’s a lot of meat in this book to digest but the language of the book is relatively simple and straightforward, making it easier to get through than its size and scope might suggest.