  This monograph describes a Riemannian geometric reduction approach to the
three-body problem. The fundamental theorems are presented in the introductory
part, whereas their proofs are provided in later chapters where specific topics
are analyzed in more detail. The basic idea is to reduce the kinematic and
dynamics of mass triangles to the congruence moduli space and the shape space,
representing SO(3)-congruence and similarity classes respectively.In
particular, the Euler equations for mass triangle motions are worked out,
generalizing the classical Euler equations for rigid body motions. The last
chapters are devoted to the study of Newtonian triple collision motions, in the
above geometric setting, and their shape curves are analyzed in special cases.
