  We prove that $\mathcal{C}^2$ surface diffeomorphisms have symbolic
extensions, i.e. topological extensions which are subshifts over a finite
alphabet. Following the strategy of T.Downarowicz and A.Maass \cite{Dow} we
bound the local entropy of ergodic measures in terms of Lyapunov exponents.
This is done by reparametrizing Bowen balls by contracting maps in a approach
combining hyperbolic theory and Yomdin's theory.
