Wavelets have been shown to be an extremely powerful tool for signal processing. Lately they have also been applied to theoretical physics. In this talk I will introduce wavelets and point out some applications of wavelets for studying dynamical systems, in particular dynamical systems occurring in quantum statistical mechanics. During the talk I will discuss the commutation relation AB=BF(A) for two bounded operator A and B and some function F( ). It will be demonstrated how this commutation relation is related to dynamical systems, quantum statistical mechanics and representations of wavelets. The talk will not assume any prior knowledge about wavelets.