This book provides a systematic mathematical analysis of entropy and stochastic processes, especially Gaussian processes, and its applications to information theory. The contents fall roughly into two parts. In the first part the main emphasis is on entropy; a unified treatment of entrop in information theory, probability theory and mathematical statistics is presented. The second part deals mostly with information theory for continuous communication systems, based on the most recently available methods in probability theory, and the analysis developed in the first part. Particular emphasis is placed on the Gaussian channel which is the most important continuous communication channel. An advantage of this book is that, unlike most books on information theory, it places emphasis on continuous communication systems, rather than discrete ones.