Probability and random processes play a central role in the characterization, design, and performance analysis of digital communication systems. Due to the presence of noise, interference, and other transmission impairments, the behavior and performance of digital communication systems are probabilistic in nature. This chapter begins with the basic axioms and concepts of probability. Then, discrete and continuous random variables are introduced along with their means, variance, and moments, followed by bivariate or pairs of random variables. Communication systems often involve functions of random variables, so functions of a single random variable and functions of two random variables are considered. Finally, the chapter presents a variety of discrete probability distributions and continuous probability density functions that are useful for describing communication signals, communication channels, and analyzing the performance of digital communication systems.