Introduction to the Fast Multipole Method introduces the reader to the theory and computer implementation of the Fast Multipole Method. It covers the topics of Laplace's equation, spherical harmonics, angular momentum, the Wigner matrix, the addition theorem for solid harmonics, and lattice sums for periodic boundary conditions, along with providing a complete, self-contained explanation of the math of the method, so that anyone having an undergraduate grasp of calculus should be able to follow the material presented. The authors derive the Fast Multipole Method from first principles and systematically construct the theory connecting all the parts.Key FeaturesIntroduces each topic from first principlesDerives every equation presented, and explains each step in its derivationBuilds the necessary theory in order to understand, develop, and use the methodDescribes the conversion from theory to computer implementationGuides through code optimization and parallelization