  In this thesis we study the Seiberg-Witten theory of an oriented homology
3-sphere. The goal is to extract topological invariants - the Seiberg-Witten
invariants - by counting the solutions to the Seiberg-Witten equations on the
manifold. The first question we consider is whether the Seiberg-Witten
invariants depend on the geometric or analytic data involved in their
definition. In the first main result of this thesis, we completely determine
the dependence of the Seiberg-Witten invariants on the data involved in their
definition. In particular, we show that even for the simplest manifold, the
3-sphere $S^3$, the Seiberg-Witten invariants take infinitely many different
values.
  The rest of this thesis is devoted to understanding the Seiberg-Witten
invariants in a specific geometric setting - the surgery setting. In that
context we prove a gluing formula, which identifies the Seiberg-Witten
invariants as certain ``homological intersection numbers''.
