One of the beautiful branches of mathematics. You will see how we study symmetry. Topics to be covered are basic group, ring and field theory.
Only discuss Groups:
- Armstrong M.A. Groups and Symmetry - 'Numbers measure size, groups measure symmetry,' said the author. This book deals with several topics, which introductory abstract algebra texts usually skip, like Platonic solid and wallpaper patterns.
- Baker A. Groups, Symmetry and Fractals (FREE!)
- Law L.M.E. Group Theory [.pdf] (FREE!)
- Milne J.S. Group Theory (FREE!)
Rings and Fields:
- Chambert-Loir A. A Field Guide to Algebra
- Ellis G. Rings and Fields
- Mitchell J. Rings and Fields (FREE!)
- Skorobogatov A.N. Rings and Fields Lecture Notes [.pdf] (FREE!)
- Anderson M. and Feil T. A First Course in Abstract Algebra: Rings, Groups, and Fields
- Arapura D. Abstract Algebra Done Correctly [.pdf] (FREE!)
- Artin M. Algebra - Not aimed at this level, but this is the one you like to keep in your own library. As M. Artin states in "A Note for the Teacher" that several sections would make a coherent course, you may simply follow his list at this stage. My lecturer recommended this partly because M. Artin was his supervisor, I recommend this but I have no direct relationship with M. Artin.
- Beachy J.A. and Blair W.D. Abstract Algebra Online Study Guide (FREE!)
- Birkhoff G. and Mac Lane S. A Survey of Modern Algebra
- Blomqvist C. Algebraic Systems (FREE!)
- Chan D. Higher Algebra Lecture Notes [.pdf] (FREE!) - Diagram omitted, it's best to attend Daniel's lecture.
- Clark A. Elements of Abstract Algebra - Kind of handbook.
- Connell E.H. Elements of Abstract and Linear Algebra (FREE!)
- Dummit D.S. and Foote R.M. Abstract Algebra - If you could afford this. Standard recommended text in the U.S. Read sections recommended by the authors in the preface, leave others to the next stage. See Foote's web for errata.
- Fraleigh J.B. A First Course in Abstract Algebra - Fraleigh made it, he gives a good introduction abstract algebra for newbie. Ideal for a first coures. See also Afra's incomplete notes [.pdf].
- Garrett P. Intro to Abstract Algebra [.pdf] (FREE!)
- Gilbert W.J. Modern Algebra with Applications
- Gillian J.A. Contemporary Abstract Algebra - As the author have said, this book includes 'lines from popular songs, poems, quotations, biographies, historical notes, hundreds of figures, dozens of photographs, and numerous tables and charts." If you prefer those things. See the author's website for resources.
- Goodman F.M. Algebra: Abstract and Concrete (FREE!)
- Herstein I.H. Abstract Algebra
- Ikenaga B. Abstract Algebra (FREE!)
- Jacobson N. Basic Algebra I - New edition of his Lectures in Abstract Algebra.
- Knapp A.W. Basic Algebra - See the web for correction.
- Rotman J.J. A First Course in Abstract Algebra - Check out Rotman's page for errata.
- Shahriari S. Lectures on Algebra I [.pdf] (FREE!)
- 李華介：大學基礎代數 (FREE!) - The best free material on introductory abstract algebra I have seen so far, provided you can read Chinese.