This course serves to illustrate important principles in Monte Carlo simulations and to demonstrate the power of Monte Carlo methods in simulation applications. Many basic ideas in classical Monte Carlo computations, including the Metropolis-Hastings algorithm, the Gibbs sampler, Markov Chain Monte Carlo, the acceptance-rejection method, Monte Carlo integration, quasi-Monte Carlo, random number generation, will be introduced. Then the focus shifts to applying these methods to scientific computing simulations in high-performance computing environment such as tightly coupled parallel computers, clusters, and grid-computing environments. Applications to Bayesian computation, molecular dynamics, computational biology, computational material, VLSI chip design and optimization, and nuclear simulation will be illustrated.