Waiting is inherently related to many situations that we encounter in practice. Some examples of such practical situations are production systems, transportation and stocking systems, communication systems, and health care systems. Queuing models are beneficial for the design of these systems in terms of layout, capacities and control. In this course, we focus on the mathematical analysis of several elementary queueing models. Specifically, as waiting primarily occurs due to randomness in the arrival and service processes of customers, queueing theory is embedded in the field of applied probability. We mainly pay attention to methods for the analysis of queueing models, but also to their applications.