Introductory Group Theory Book Recommendation

Question

I am looking for an introductory book on group theory as I would like to know more about the subject. I am aware that this an extremely useful area of mathematics. What book would you suggest for a first course on group theory?

For some advice how to ask about book recommendations, see here (and in other posts on meta.) — Martin Sleziak, Oct 24 '15 at 05:32
It might be worth checking other questions tagged group-theory+book-recommendation or group-theory+reference-request. — Martin Sleziak, Oct 24 '15 at 05:33
There's a thread here that received some attention, but which was closed: http://math.stackexchange.com/questions/25506/introductory-group-theory-textbook — littleO, Oct 24 '15 at 11:52

score 3 · Answer 1 · edited Oct 24 '15 at 12:07

3

A Book of Abstract Algebra, by Charles C. Pinter, is famous for being clear, accessible, and doing a lot of hand-holding.

edited Oct 24 '15 at 12:07

leonbloy

66,202

answered Oct 24 '15 at 05:32

goblin GONE

69,385

score 3 · Answer 2 · answered Oct 24 '15 at 11:27

3

Contemporary Abstract Algebra by Joseph Gallian is written especially for beginners which is full of motivations- motivations for the subject, motivations for a topic, motivations behind a theorem, motivations for exercises, etc.

The exercises range from very elementary to difficult. They always keep the beginner-reader in touch with the subject.

answered Oct 24 '15 at 11:27

Groups

10,534

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One should always be suspicious towards text books that have $10$ editions, and going strong. – uniquesolution Feb 01 '22 at 23:32

score 2 · Answer 3 · answered Oct 24 '15 at 11:33

2

Visual Group Theory is full of motivation and illustrated examples, and comes with a companion interactive tool Group Explorer.

answered Oct 24 '15 at 11:33

Weaam

2,888

score 2 · Answer 4 · answered Oct 24 '15 at 13:01

2

If you want a leisurely pace, try Budden's The Fascination of Groups.

answered Oct 24 '15 at 13:01

lhf

221,500

luisfelipe18 · Answer 5 · 2022-02-22T01:18:37.893

1

Abstract algebra - Herstein is good to start in groups, it starts with basic previous requeriments and has a lot of good examples and exercises that helps to discover the next themes, it has 3 levels of problems, start with 1,2 difficult level problems and you'll be ok.

Algebra-Serge Lang, ed.Springer is a complete book for Algebra for people who know some algebra from before , also if you read some spanish, there are some easy and complete free books of algebra. Look for "algebra-Carlos Ivorra Castillo" (oriented to number theory) or "cuadernos de algebra- Oswaldo Lezama" with a google search (more general, there are 10 books which takes since groups to homological algebra).

edited Feb 22 '22 at 01:18

answered Oct 24 '15 at 12:27

luisfelipe18

3,690

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Lang's Algebra is not "an extremely basic opener book", not even close! Sorry! – Weaam Oct 24 '15 at 12:55
@Weaam okey, I wrote because we use this in pregrade in UNI- Lima Perú. But as you say, is not so opener book you right, let me edit. – luisfelipe18 Oct 24 '15 at 13:01
1

@Weaam thanks to you, other users don't give reasons to downvotes ;) – luisfelipe18 Oct 24 '15 at 13:11

score 1 · Answer 6 · answered Oct 24 '15 at 13:07

You might find it to your benefit to go a more concrete route with these very detailed notes on permutation puzzles- http://www.sfu.ca/~jtmulhol/math302/notes/302notes.pdf

You could alternatively try Visual Group Theory by Nathan Carter, but it may need more care than you might at first expect.

Also, if you don't mind video lectures, here's a more traditional course- http://wayback.archive-it.org/3671/20150528171650/https://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

Introductory Group Theory Book Recommendation

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