A geometrical interpretation of the parallel composition is considered in order to investigate various properties of these operations. The approach provides the possibility to introduce in a natural way, and to study, important concepts like determinism, order (priority), communication, bisimulation, fairness, re-entrance, composability, etc.

Some new and interesting problems of research are presented in connection with fields like concurrency, formal languages and automata, algebra, and combinatorics. As a consequence, there are useful applications to concurrency where parallel composition of processes is a fundamental operation.

The talk is self contained, no previous knowledge is assumed.