This course is an introduction to Bayesian inference and Markov Chain Monte Carlo computational methods. We begin with an overview of the principles of Bayesian inference and study a number of classic conjugate models. Students then learn the basic concepts of Markov chains and their convergence to an equilibrium distribution. Finally, we explore the celebrated Metropolis-Hastings algorithm and the Gibbs sampler, and see how these can be used to estimate a variety of Bayesian models. All coursework is completed using the R programming language in the RStudio environment. No prior knowledge of Bayesian inference is required, nor is familiarity with R assumed.