  This is a short note on the relation of the Matrix model with the
non-commutative geometry of the 11-dimensional supermembrane. We put forward
the idea that M-theory is described by the 't Hooft topological expansion of
the Matrix model in the large N-limit where all topologies of membranes appear.
This expansion can faithfully be represented by the Moyal Yang-Mills theory of
membranes. We discuss this conjecture in the case of finite N, where the
non-commutative geometry of the membrane is given be the finite quantum
mechanics. The use of the finite dimensional representations of the Heisenberg
group reveals the cellular structure of a toroidal supermembrane on which the
Matrix model appears as a non-commutatutive Yang-Mills theory. The Moyal star
product on the space of functions in the case of rational values of the Planck
constant \hbar represents exactly this cellular structure. We also discuss the
integrability of the instanton sector as well as the topological charge and the
corresponding Bogomol'nyi bound.
