The organization of this thesis is as follows. In chapter 2 we introduce the basic ingredients of string theory. Chapter 3 discusses supersymmetry algebras and the concept of BPS states. In the same chapter we also introduce the different eleven– and ten–dimensional supergravity models, the BPS soliton solutions of these models and present the concepts of string duality and M–theory. This will provide the necessary background material to move on to chapters 4 and 5. Chapter 4 introduces Matrix theory as a candidate description of M–theory and discusses the construction of (part of) the BPS spectrum in Matrix theory. This BPS spectrum is then compared to (part of) the BPS spectrum of M–theory. In chapter 5 we discuss a general approach to consider non–trivial low energy limits of string theory in the background of p–brane soliton solutions. The resulting duality relations are discussed and some new examples are presented. Finally in the concluding chapter 6 we summarize and discus our results and try to establish a
connection between Matrix theory and the dualities obtained in chapter 5.