An invitation to general algebra and universal constructions / George M. Bergman

This course develops concepts and results which occur repeatedly throughout the various areas of algebra, and sometimes in other fields of mathematics as well, and which can provide valuable tools and perspectives to those working in these fields (there is a strong emphasis on examples and instructive exercises). The notes are divided into 10 chapters: About the course, and these notes, Making some things precise, Free groups, A Cook's tour of other universal constructions, Ordered sets, introduction, and the Axiom of choice, Lattices, closure operators and Galois connections, Categories and functors, Universal constructions in category-theoretic terms, Varieties of algebras and algebra and coalgebra objects in categories, and functors having adjoints. The study of this book assumes only an elementary background in algebra, corresponding to an honors undergraduate algebra course or one semester of graduate algebra, plus a moderate level of mathematical sophistication. (Zentralblatt)