Differential-algebraic equations are becoming increasingly important in a
lot of technical areas, such as electrical engineering. Since they are not
explicitly solvable in most cases, or have hardly manageable solutions, and
solutions even need not to be unique, one focuses on qualitative statements
about the system behavior. Stability of linear time-varying
differential-algebraic equations of the form $E(t) \dot x = A(t)x+f(t)$ is
studied in this thesis. A detailed investigation of such systems without
any restrictions seems not to be available. A main goal of this thesis is
to develop a relationship between the stability behavior of the solutions
of this system and the stability behavior of the trivial solution of its
associated homogeneous system. Furthermore, we develop, via a
Lyapunov-approach, conditions for a restricted form of exponential
stability. Moreover, we give a detailed investigation of the solution and
stability theory of systems which are transferable into standard canonical
form. Regarding this we state a representation of the general solution and
a condition under which it exists. We introduce consistent initial values
and, for homogeneous systems, the generalized transition matrix and
determine properties of it, which can be seen as direct generalizations of
the properties of the transition matrix of an ordinary linear differential
equation. Furthermore, we introduce the projected generalized time-varying
Lyapunov-equation, and derive necessary and sufficient conditions for
exponential stability utilizing this equation. In this context the
solvability of the Lyapunov-equation as well as the uniqueness and
representation of its solution is investigated.