Mikhalev A., Pilz G. The Concise Handbook of Algebra 2002

Textbook in PDF format

It is bу no means clear what comprises the "heart" or "core" of algebra, the part of algebra which every algebraist should know. Hence we feel that а book on "our heart" might bе useful. We have tried to catch this heart in а collection of about 150 short sections, written Bу leading algebraists in these areas. These sections are organized in 9 chapters А, В...
1. Of course, the selection is partly based on personal preferences, and we ask you for your understanding if some selections do not meet your taste (for unknown reasons, we only had proЫems in the chapter "Groups" to get enough articles in time). We hope that this book sets up а standard of what all algebraists are supposed to know in "their" chapters; interested people from other areas should Bе аЫе to get а quick idea about the area. So the target group consists of anyone interested in algebra, from graduate students to estaЫished researchers, including those who want to oBtain а quick overview or а better understanding of our selected topics. The prerequisites are something like the contents of standard textbooks on higher algebra. This book should also еnаblе the reader to read the "big" Handbook (Hazewinkel 1999-) and other handbooks.
Semigroups
Groups
Rings, Modules, Algebras
Fields
Representation Theory
Lattices
Universal Algebra
Homological Algebra
Miscellaneous