This book stems from lectures given at the Max-PlanckInstitut
fÜr Mathematik (Bonn) during the winter semester
1985/1986 under the title "Fuchsian Differential Equations".
The aim of this series of lectures was to study linear
ordinary differential equations and systems of linear partial
differential equations with finite dimensional solution spaces
in the complex analytic category; referred to in the course of
this book as differential equations. This field has a long
history and has attracted many farnaus mathematicians such as
Euler, Gauss, Schwarz and Kummer, for example. Cauchy, L. and
R. Fuchs, Painleve, Riemann, Poincare and Birkhoff were also
interested in these equations. In many text books, as for
instance in [Bie], in [Huk] and in [Inu], one can find the
classical results in this direction, while the most recent ones
are to be looked for in the book edited by Gerard and Okamoto
[G-0].