The main focus of this thesis is the data-driven analysis of complex dynamical systems. Although we will consider mainly molecular dynamics and fluid dynamics problems, the presented methods can be applied to arbitrary dynamical systems. In fact, in order to apply these methods, no a priori knowledge about the system is required, only simulation or measurement data. Such data-driven methods got a lot of attention recently due to the availability of large data sets. Gaining insight into the characteristic properties of a system by analyzing such data sets is akin to the metaphorical search for a needle in a haystack. The goal of data-driven methods is to extract relevant information about global properties of the underlying system, whose governing equations might be unknown. Global information can be obtained by analyzing the eigenvalues and eigenfunctions of transfer operators associated with the system.
