  Noncommutative lattices have been recently used as finite topological
approximations in quantum physical models. As a first step in the construction
of bundles and characteristic classes over such noncommutative spaces, we shall
study their $K$-theory. We shall do it algebraically, by studying the algebraic
$K$-theory of the associated algebras of `continuous functions' which turn out
to be noncommutative approximately finite dimensional (AF) $C^*$-algebra . We
also work out several examples.
