We consider nonlinear systems with inputs. Each system is assumed to be stable in a certain sense, that will be explained. Our main question is whether an interconnection of these systems remains stable. We will start with introduction of input-to-state stability (ISS) notion and known facts about ISS systems and illustrate them with simple examples. A sufficient condition for the stability of an interconnection of systems will be given and discussed. A constructive method of finding a Lyapunov function will be shown. We will see how the derivation of our main results is related to monotone operators and some purely topological problems. In the end we will provide several application examples of the main results coming from different engineering problems