Multivariate characteristic functions are the Fourier transforms of distributions of random vectors. They represent an important tool for the study of ifferent problems of probability theory, e.g. limit theorems, characterization problems, and description of special distributions, but they also appear as correlation functions of stationary random fields. This book provides an introduction to the theory of these functions which may be useful also for readers who want to learn about multivariate Fourier transforms. It presents some special topics and several classical and recent applications. Several appendices make the book a must have source.