This project aims to design efficient and problem tailored numerical solution methods for certain classes of MLFGs in function space accompanied by the theoretical analysis of these problems. While in a classical Nash equilibrium problem (NEP) we have several players that simultaneously make a decision which influences their own outcome and that of the others, in a multi-leader-follower game (MLFG) the group of players is split into the so-called leaders deciding first and followers reacting to this. This hierarchical game has various applications e.g. in telecommunications, traffic networks and electricity markets. It can be seen as an extension of the single-leader-multi-follower (Stackelberg) game or mathematical program with equilibrium constraints (MPEC). Though by now much is known about NEPs and MPECs in finite dimensions and lately also in function space, this is not the case for MLFGs. We start with the theoretical investigation (existence, uniqueness and suitable approximations of Nash equilibria) of finite-dimensional (i.e. static) MLFGs. Next, we will develop new numerical methods for the static MLFGs, that admit solutions, which avoid the drawbacks of existing methods. These outcomes of the first period of the project are not only of interest by themselves, but will serve us in the main part as starting point for the theory as well as the design of numerical solution methods for the dynamic (time-dependent) MLFG. Additionally, in parallel, applications will be considered to build a test library for our algorithms that will also be made publicly available.