Queueing phenomena occur everywhere: in road traffic, production processes, call centers, health centers, and in computer and communication systems. Random fluctuations in the offered traffic/work are a major cause of delays. Probability theory is used to model such queueing phenomena and analyse their impact on system performance. In this course, we set the methodological foundations (including Markov chains, Markov processes, Poisson processes, and renewal theory) for the performance analysis and optimization of queueing systems.