Lecture Notes
Group Theory
Much part of these lecture notes came from Modern Algebra (Group Theory) course I taught.
These lecture notes should be accessible by undergraduate students of mathematics or physics who have taken Linear Algebra.
Lecture Notes
Problem Sets
References and Further Reading
Click on linked topics to view lecture notes.
An Overview
Functions
Basic Number Theory
Examples of Groups
Subgroups
Laglange's Theorem
Congruence Modulo \(n\)
Homomorphisms
Normal Subgroups
Quotient Groups
The Isomorphism Theorems
Direct Products
Finitely Generated Abelian Groups
Click on the following links for problems.
Basic Number Theory
Examples of Groups
Subgroups
Laglange's Theorem
Congruence Modulo \(n\)
Homomorphisms
Normal Subgroups
Quotient Groups
The Isomorphism Theorems & Direct Products
Stanley N. Burris and H. P. Shankappanavar, A Course in Universal Algebra, Graduate Texts in Mathematics, Springer-Verlag, 1981
This book is not about group theory but if you are interested in studying general algebra beyond group theory, this is a wonderful book which can be downloaded for free from the website of Stanley N. Burris (linked above). Simply speaking, universal algebra studies algebras themselves rather than models of algebras such as groups, rings, etc.
John B. Fraleigh, A First Course in Abstract Algebra, 7th Edition, Pearson, 2002I. N. Herstein, Abstract Algebra, 3rd Edition, Wiley, 1996
I. N. Herstein, Topics in Algebra, 2nd Edition, John Wiley & Sons, 1975