  Given a compact Riemannian manifold $(M g)$ and Morse function $f:m\to
\mathbb{R}$ whose gradient flow satisfies the Morse-Smale condition, (i.e. the
stable and unstable manifolds of f intersect transversely) we construct a chain
complex called the Morse-Witten Complex. Our goal on this paper is show that
the homology of the Morse-Witten complex is isomorphic to the singular homology
of $M$.
