An Invitation to General Algebra and Universal Constructions

George M. Bergman is Professor Emeritus of Mathematics at the University of California, Berkeley. He has published over 100 research articles in logic, ring theory, universal algebra, and category theory.

1 About the course, and these notes.- Part I: Motivation and Examples.- 2 Making Some Things Precise.- 3 Free Groups.- 4 A Cook's Tour.- Part II: Basic Tools and Concepts.- 5 Ordered Sets, Induction, and the Axiom of Choice.- 6 Lattices, Closure Operators, and Galois Connections.- 7 Categories and Functors.- 8 Universal Constructions.- 9 Varieties of Algebras.- Part III: More on Adjunctions.- 10 Algebras, Coalgebras, and Adjunctions.- References.- List of Exercises.- Symbol Index.- Word and Phrase Index.

"The aim of this book is to survey the basic notions and results of general algebra; also, it is a detailed and self-contained introduction to general algebra from the point of view of categories and functors. ... The author takes care in writing full proofs throughout the book and he shows also ways of possible applications. The text contains a wealth material and should serve as a textbook for readers interested in this field." (Danica Jakubíková-Studenovská, zbMATH 1317.08001, 2015)