The present book gives an account of the theory of commu­ tative normed rings with applications to analysis and topology. The paper by I. N. Gelfand and M. A. Naimark Normed Rings with an Involution and their Representations, which is presented here as Chapter VIII, may serve as an intro­ duction to the theory of non-commutative normed rings with an involution.The book is addressed to mathematicians—students in ad­ vanced courses, research students, and scholars—who are interested in functional analysis and its applications.