Dowd M. Introductory Algebra, Topology, and Category Theory 2006

Textbook in PDF format

This text is meant to serve as a introduction to abstract algebra for advanced undergraduates. There are many introductions to abstract algebra, so a new one should have some distinguishing characteristics. The main distinguishing characteristics of this text are the coverage of universal algebra and category theory, and their use in the introductory presentation of topics in algebra; and the coverage of various topics outside the main line of classical abstract algebra…
Indeed! This is not for your typical Abstract Algebra course. In many ways, this is a refreshing book. The perspective it brings is that universal properties provide a useful set of organizing principles, giving both structure and flexibility to one's study. Impressed with the topics covered. From sections on algebraic geometry and algebraic number theory to model theory and computability to homology.
Universal algebra
Orders
Groups
Permutation groups
Rings
Polynomials
Modules
Fields
Linear algebra
Model theory
Computability
Category theory
Conjugacy
Characters
Series
Topological spaces
Tensor algebra
Homology
Further topics in rings and fields
Lattice orders
Convexity
Point lattices
Algebra and Topology
Algebraic geometry
Algebraic number theory
Lie groups
Some algorithms
Appendicies
Set theory
Basic linear algebra
Basic graph theory