The proposed book is a textbook on probability and random processes for first- and second-year graduate students in engineering.?It will assume basic prior knowledge of probability and random processes at the undergraduate level. The goal is to provide a more rigorous understanding of probability (via measure theory and fields) and random processes (with extensive coverage of correlation and its usefulness).This book will provide the background necessary for the study of such topics as digital communications, information theory, adaptive filtering, linear and nonlinear estimation and detection, etc. The material will be presented in such a manner that the important points are clearly explained, and key examples are presented with graphical interpretations.?Advanced topics (such as convergence and stochastic calculus) and important applications (such as estimation, detection, and adaptation) will be covered.