This is part of a larger project that aims to develop a program able to simulate problems with millions of degrees of freedom on a personal computer. The Fast Multipole Method (FMM) is combined with the Expedite Boundary Element Method (EBEM) for integration, in the project s final version, with iterative equations solvers. The EBEM is especially advantageous when applied to problems with complicated topology as well as in the case of highly complex fundamental solutions. In this work, a FMM formulation is proposed for the use with virtually any type of fundamental solution and considering curved boundaries, which seems to be an original contribution. This formulation presents a more compact format than the ones shown in the technical literature, and can be directly applied to different kinds of problems without the need of manipulation of its basic structure, being numerically validated for a few applications. Its application in the context of the EBEM leads to the straightforward implementation of higher-order elements for generally curved boundaries that dispenses integration when the boundary segment is relatively far from the source point.