The discipline of Economics and Finance contains many applications of the theory of stochastic processes. Exposing an aspiring undergraduate student to these ideas will enrich their understanding of the discipline. However, our undergraduate curricula have limited exposure to mathematical thinking, which impedes reading standard texts on this matter. This text aims to cover select topics in i.i.d processes, Markov chains, Poisson processes, Weiner processes, martingales, and Brownian motion in an expository manner. While few theorems are proved, the focus is on application and computation. Applications to ruin theory (Cramer-Lundberg model), inventory management, and asset pricing will be covered. Ample numerical examples will be presented.