This book provides a self-contained and systematic treatment of stochastic processes and their applications. Having a basic knowledge of mathematics at an undergraduate level, the reader should be able to understand stochastic processes with discrete state space such as Poisson processes renewal processes and Markov chains. Fruitful applications of such processes are also described in the real world problems in reliability and queueing models. Numerous illustrations are included for better understanding. Problems are included in each chapter. Appendices are devoted to the Laplace-Stieltjes transforms and their properties, and answers to selected problems. It is suitable for an introductory one-semester or two-quarter course in stochastic processes for the junior or senior undergraduate students.