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We define the contact homology algebra for any contact manifold and show thatit is an invariant of the contact manifold. More precisely, given a contactmanifold $(M,\xi)$ and some auxiliary data $\mathcal{D}$, we define an algebra$HC(\mathcal{D})$. If $\mathcal{D}_1$ and $\mathcal{D}_2$ are two choices ofauxiliary 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.

Semi-global Kuranishi charts and the definition of contact homology