  This paper introduces the notion of a stability condition on a triangulated
category. The motivation comes from the study of Dirichlet branes in string
theory, and especially from M.R. Douglas's notion of $\Pi$-stability. From a
mathematical point of view, the most interesting feature of the definition is
that the set of stability conditions $\Stab(\T)$ on a fixed category $\T$ has a
natural topology, thus defining a new invariant of triangulated categories.
After setting up the necessary definitions I prove a deformation result which
shows that the space $\Stab(\T)$ with its natural topology is a manifold,
possibly infinite-dimensional.
