"This monograph is devoted to various types of algebras of functions with n variables. It is the first complete monograph (in English) on this area, covering mainly Russian literature. It aresses all algebraist working in the area of universal algebras, semigroup theory. It is also fruitful source for graduate and PhD students who are starting their research in this area. The book is the first monograph in English mathematical literature which provides readers with a very systematical study of the notion of Menger algebras and its generalizations and applications. The results presented here were originally published mostly in Russian literature: In 2006 the first version of this book was edited in Russian; now is presented an extended version. Two big new and very important chapters are added. The monograph is a very good survey of unknown or little-known Russian literature on algebras of multiplace functions. It uncovers to the mathematical community a beautiful and strongly developing theory."--Publisher's website.