This course provides an introduction to Monte Carlo methods with applications in Bayesian computing and rare event sampling. Topics include Markov chain Monte Carlo (MCMC), Gibbs samplers, Langevin samplers, MCMC for infinite-dimensional problems, convergence of MCMC, parallel tempering, umbrella sampling, forward flux sampling, and sequential Monte Carlo. Emphasis is placed both on rigorous mathematical development and on practical coding experience. Not offered 2026-27.