The sheaf concept is part of the basic vocabulary of modern geometry and topology. It serves to formalise the transition from the local to the global. However, sheaf theory is much more general; it can even be used to study the foundations of logic. These statements already indicate the generality of the theory. Therefore, we will only try to introduce the basic ideas here leisurely, without claiming to deploy the category-theoretical machine properly. We will naturally not get as far as, for example, the book [MM94], which is well suited for further education in this direction.