The basic concepts of algebra. 3rd edition, corrected. Shafarevich I.R.

The work is devoted to the review of the basic concepts, ideas and directions of algebra. Its goal is to give an idea of ​​the spirit of algebra and its connections with other parts of mathematics. Particular attention is paid to the motivation for algebraic concepts and setting tasks.

The reader is supposed to own linear algebra and the basics of analysis. Other concepts used are determined with the exception of some isolated examples that are found when analyzing. Starting from the presentation and explanations of the simplest concepts-fields, rings, modules, groups, work leads to a review of more complex theories: group representations, algebris, homological algebra, k-theoria.

The book is intended for a wide range of specialists, students, graduate students of physical and mathematical specialties.