### Abstract:

A short exposition of quantum statistical mechanics for certain simple physical systems is given in Chapter 2. In particular the equilibrium states of such systems are discussed. In Chapter 3 it is shown that the equilibrium states of these systems are exactly the so-called KMS states. KMS states are then suggested as the equilibrium states of more general systems. Chapter 4 is devoted to the Tomita-Takesaki theory. This theory initially seems completely separate from KMS states, but in section 4.4 it is shown that there is actually a strong connection between the two. This connection can be viewed as the central result of this dissertation since it enables us to understand the physical meaning of a large part of the Tomita-Takesaki theory, namely that the time-evolution of a physical system in equilibrium can be expressed in terms of the Tomita-Takesaki theory. That an abstract mathematical theory such as the Tomita-Takesaki theory has a simple physical interpretation is the motivation for this dissertation.