The N-body problem of 6n-12 degrees of freedom with twelve inherent constraints creates a difficult situation in working the equations of motion for three or more masses. This necessitates the mathematical physicist remedying the situation by determining proper constraints to get past this dilemma by requiring a specialized set of conditions to define a unique problem.This book addresses these issues and provides a general approach to solving certain classes of n-body problems, thereby showing that there exists a large body of mass configurations that can be formulated and solved deterministically. The problems provided at the end of each chapter will allow the reader to progress at a measured rate in understanding binary, trinary, and quadruple structured configurations, as well as subsystem perturbations, particle velocities, state vectors, period ratios, and sphere of influence.As an everyday resource in the working environment, this book gives the reader the prerequisite tools to deal with n-body configuration structures, whether in the real universe or in pursing purely theoretical problems.