  In this paper we give a complete topological classification of orientation
preserving Morse-Smale diffeomorphisms on orientable closed surfaces. For MS
diffeomorphisms with relatively simple behaviour it was known that such a
classification can be given through a directed graph, a three-colour directed
graph or by a certain topological object, called a scheme. Here we will assign
to any MS surface diffeomorphism a finite amount of data which completely
determines its topological conjugacy class. Moreover, we show that associated
to any abstract version of this data, there exists a unique conjugacy class of
MS orientation preserving diffeomorphisms (on some orientation preserving
surface). As a corollary we obtain a different proof that nearby MS
diffeomorphisms are topologically conjugate.
