The first part of the present exposition is devoted to the theory of Toeplitz forms. The second part deals with applications, in particular to the calculus of probability and mathematical statistics. Neither part claims completeness in any way. The purpose has been to elucidate the principal ideas of this remarkable chapter of modern analysis and to help the interested student of mathematical statistics to acquire a working knowledge of the subject. The somewhat protracted Chapter 1 explains not only the notation employed but contains also the definition of important auxiliary concepts and the exposition of basic results which will be used later. This arrangement avoids interruptions in the main text. It is assumed that the reader is in possession of the fundamental facts of the theory of functions.