Six decades after the first simulation in physics, simulations became a tool that have invaded all fields of sciences. The lecture starts by an overview of basic methods of molecular dynamics and Monte-Carlo simulations. In a second part, we consider various observables that are available in simulations. A third part is dedicated to the investigation of phase transitions by implementing finite size analysis, reweighting method, as well as several advanced Monte-Carlo methods (tempering, Wang-Landau, cluster algorithm). In a fourth part, we consider small systems with Brownian dynamics and the relevant role of fluctuations in the framework of large deviation function, fluctuation theorems and stochastic thermodynamics. In the last part, we propose an introduction to non-equilibrium simulations by considering some paradigmatic models and simulation methods for non Hamiltonian systems.