  In this paper we consider the problem of quantizing theories defined over
configuration spaces described by non-commuting parameters. If one tries to do
that by generalizing the path-integral formalism, the first problem one has to
deal with is the definition of integral over these generalized configuration
spaces. This is the problem we state and solve in the present work, by
constructing an explicit algorithm for the integration over a general algebra.
Many examples are discussed in order to illustrate our construction.
