For many mathematical investigations the notion of

integrability in the sense of Riemann, which is used in the basic courses, is insufficient. Above all, it is difficult to guarantee

that the limit of a sequence of Riemann integrable functions is an integrable function. The aim of the course is to acquaint the postgraduate student with the Lebesgue integral, and important theorems valid for it. This theory is indispensable for researchers in, e.g., mathematical analysis, numerical analysis or stochastic processes.