A survey of degree theory: Basis and development

In the first part of this survey the author discusses the basic ideas of degree theory and describes some applications of the Brouwer and Leray-Schauder degrees. The second part briefly describes the extension of the theory to cover successively wider classes of mappings. The references to both parts are given at the end of part II: The reader is frequently referred to some of these references for more details, and particularly to [14].