  In this master's thesis, we introduce expansion systems as a general
framework to describe a large variety of approximation algorithms, such as
Taylor approximation, decimal expansion and continued fraction. We consider
some basic properties of expansion systems, and also study criteria for
convergence. Further, we introduce the notion of isomorphisms between expansion
systems. In the appendix, we discuss another class of expansion systems, which
we call approximation systems. Many claims of convergence in this appendix,
remain to be proven.
