The aim of the tutorial is to give a general overview of the Membrane Computing paradigm [2,5]. Membrane Computing is a quite active research field, initiated by Gh. Păun in 1998 [3]. It is a theoretical machine-oriented model, where the computational devices (known as P systems) are in some sense an abstraction of a living cell. There exist a large number of different definitions of P systems, but most of them share some common features: a membrane structure (defining in a natural way a number of regions or compartments), and an alphabet of objects that are able to evolve and/or move within the membrane structure according to a set of rules (emulating the way substances undergo biochemical reactions in a cell).