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 aconnection between Matrix theory and the dualities obtained in chapter 5.