In this course we will study stochastic models commonly used to analyse the performance of dynamic systems. Markov models and queues are used to study the behaviour over time of a wide range of systems, from computer hardware, communication systems, biological systems, epidemics, traffic networks to crypto-currencies. We will take a tour of the basics of Markov modelling, starting from birth-death processes, the Poisson process to general Markov and semi-Markov processes and solution methods for those processes. Then we will look at queueing models and queueing networks with exact and approximate solution algorithms. If time allows we will finally study some of the foundations of discrete event simulation.