This course introduces basic concepts of stochastic processes. The focus of the course is on the principal stochastic or random processes most commonly used in applications as mathematical models of random phenomena that evolve over time. Topics tentatively selected include: Review of conditional probability, conditional expectation, and generating functions; Markov chains in discrete time; Poisson processes; renewal processes; Markov chains in continuous time; Brownian motion and Gaussian processes. These types of processes are fundamental to modeling time-dependent random phenomena in many areas of medical and health sciences. The emphasis will be on developing a sound understanding of the material, and many of the examples of the methods will be in the area of public health and bioinformatics.