This book is and introduction to applications of the theory of stochastic processes, more specifically Markov chain theory, in popular dynamics, genetics and epidemics. A prior exposure to basic probability theory should be helpful, but by no means essential. Although this book is primarily intended for use as a textbook for a course on Applied Stochastic Processes, it can also be used by researchers in the fields of genetics or epidemics for learning about applications of probability in their respective areas.