  Motivated by some results in classical differential geometry, we give a
constructive procedure for building up a connection over a (twisted) tensor
product of two algebras, starting from connections defined on the factors. The
curvature for the product connection is explicitly calculated, and shown to be
independent of the choice of the twisting map and the module twisting map used
to define the product connection. As a consequence, we obtain that a product of
two flat connections is again a flat connection. We show that our constructions
also behaves well with respect to bimodule structures, namely being the product
of two bimodule connections again a bimodule connection. As an application of
our theory, all the product connections on the quantum plane are computed.
