In 1963 [Ann. of Math. 78, 267-288], Gerstenhaber invented acomp(osition)calculus in the Hochschild complex of an associative algebra. In this paper, the first steps of the Gerstenhaber theory are exposed in an abstract (comp system) setting. In particular, as in the Hochschild complex, a graded Lie algebra and a pre-coboundary operator can be associated to every comp system. A derivation deviation of the pre-coboundary operator over the total composition is calculated in two ways, (the long) one of which is essentially new and can be seen as an example and elaboration of theauxiliary variables methodproposed by Gerstenhaber in the early days of the comp calculus.