Sequence of random variables which are indexed by some parameter, say time, are called stochastic processes. Systems whose properties vary in a random manner can best be described in terms of stochastic processes. Behavior of such systems is sometimes termed dynamic indeterminism. Terminology and basic definitions, elements of measure theory, and examples of stochastic processes are provided. Point processes and renewal processes are also discussed in this chapter. The theory of Markov processes is also developed. Some examples of stochastic processes like: Poisson process, shot noise process, Gaussian process, Gaussian white noise process, and Brownian motion process are also discussed. The topics discussed in the section on renewal theory are: ordinary renewal process, modified renewal process, alternate renewal process, backward and forward recurrencetimes of a renewal process, equilibrium renewal process, and equilibrium alternate renewal process. The section on Markov processes deals with discrete-time Markov chains, continuous-time Markov chains, and continuous-time Markov processes.