  We define the contact homology algebra for any contact manifold and show that
it is an invariant of the contact manifold. More precisely, given a contact
manifold $(M,\xi)$ and some auxiliary data $\mathcal{D}$, we define an algebra
$HC(\mathcal{D})$. If $\mathcal{D}_1$ and $\mathcal{D}_2$ are two choices of
auxiliary data for $(M,\xi)$, then $HC(\mathcal{D}_1)$ and $HC(\mathcal{D}_2)$
are isomorphic. We use a simplified version of Kuranishi perturbation theory,
consisting of semi-global Kuranishi charts.
