In this lecture we introduce the class of distributed parameter systems by means of some real life examples. In the second part we introduce the concept of semigroups and infinitesimal generators. A special class of strongly continuous semigroups is formed by the class of contraction semigroups. There are simple conditions for an operator to be the infinitesimal generator of such a semigroup. Finally, we how how an abstract differential equation and its solutions can related to a pde.