Based on the author's years of teaching experience, this textbook provides undergraduates with a clear and carefully paced introduction to abstract algebra. It begins with groups and rings, developing important concepts thoroughly before moving on to subrings, homomorphisms, and ideals. Later chapters then introduce a number of more advanced topics, including simple groups and extensions, Noetherian rings, universal algebra, lattices, categories, Galois theory, and coding theory. The author has included a chapter on constructing the number systems, where he gives three different proofs that transcendental numbers exist.

1.intriduction 

2.rings 

3.groups 

4.vector spaces 

5.modules 

6.the number systems 

7.further topics 

8.applications

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