An introduction to abstract algebra, including topics like group and ring theory, linear algebra and a bit of algebraic geometry and the cohomology of groups. This book arose out of courses the author taught in Abstract Algebra, Galois Theory, Algebraic Geometry, and Number Theory. It can be used for self-study or as a course textbook. It covers classic areas such as group theory, ring theory, linear algebra, Galois theory. It also covers 20th century material on Gr bner bases, category theory, division algebras over the reals (with applications of quaternions to computer graphics), and cohomology. The section on category theory also covers some multilinear and exterior algebra. This edition includes the counterexample to the Jacobi Conjecture
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