This module teaches the theoretical basics for simulation of simple stochastic systems (e.g. molecular models, ising models, diffusion in model potentials). Physical principles for stochastic trajectories and ensembles are combined with a discussion of simulation techniques that are able to generate appropriate data. In more detail, we will cover: Statistical mechanics: basis and derivations to the most important physical ensembles. Boltzmann distribution, Partition function, Expectations Monte-Carlo simulation: Theory, construction, and convergence of Monte Carlo methods for the computation of stationary expectation values Molecular dynamics simulation: Theory, construction, and convergence of MD simulations for the computation of dynamical expectation values Kinetics: Rate theories, time correlations and other time-dependent expectations