The author reviews the Fast Multipole Method (FMM) for solving the Coulom- bic potential problem. An implementation of the FMM algorithm based on the Java programming language is presented, and the process of solving the Coulombic prob- lem using the FMM is illustrated in a Java applet. It is hoped that the applet can be of pedagogical value for students new to the FMM algorithm, that the Java code can be easily extended to solve matrix-vector multiplications of other types, and that the code developed in this project can serve as a basis for a full set of Application Programming Interfaces (API) to promote and aide the integration of the FMM algorithm into larger Java-based scienti¯c computing packages. A live demonstration of the applet, the source code of the current developer's build of the Java-FMM package, and other related material including API documentation can be found online at http://www.umiacs.umd.edu/~wpwy/fmm.