The present volume aims to be a comprehensive survey on the derivation of the equations of motion, both in General Relativity as well as in alternative gravity theories. The topics covered range from the description of test bodies, to self-gravitating (heavy) bodies, to current and future observations.

Emphasis is put on the coverage of various approximation methods (e.g., multipolar, post-Newtonian, self-force methods) which are extensively used in the context of the relativistic problem of motion. Applications discussed in this volume range from the motion of binary systems -- and the gravitational waves emitted by such systems -- to observations of the galactic center. In particular the impact of choices at a fundamental theoretical level on the interpretation of experiments is highlighted.

This book provides a broad and up-do-date status report, which will not only be of value for the experts working in this field, but also may serve as a guideline for students with background in General Relativity who like to enter this field.

Preface.- The New Mechanics of Myron Mathisson and its subsequent development.- Multipolar test body equations of motion in generalized gravity theories.- Energy-Momentum Tensors and Motion in Special Relativity.- Solutions of Mathisson-Papapetrou equations for highly relativistic spinning particles.- The MPD Equations in Analytic Perturbative Form.- Center of mass, spin supplementary conditions and the momentum of spinning particles.- General Relativistic Two-Body Problem: Theory and Experiment and the Role of Hidden Momentum.- Equations of Motion of Schwarzschild, Reissner-Nordstrom and Kerr Particles.- From singularities of fields to equations of particles motion.- Motion of spinless particles in gravitational fields.- On the Strong Field Point Particle Limit and Equation of Motion in General Relativity.- Motion in classical field theories and the foundations of the self-force problem.- Motion of small objects in curved spacetimes: An introduction to gravitational self-force.- Self-force: Computational Strategies.- On the self-force in electrodynamics and implications for gravity.- Self-gravitating elastic bodies.- On geodesic dynamics in deformed black-hole fields.- Higher order post-Newtonian dynamics of compact binary systems in Hamiltonian form.- Spin and quadrupole contributions to the motion of astrophysical binaries.- Testing the motion of strongly self-gravitating bodies with radio pulsars.- Equations of Motion in an Expanding Universe.- The Galactic Center Black Hole Laboratory.- Extreme mass ratio inspirals: perspectives for their detection.- Level sets of the lapse function in static GR.- Aberrational Effects for Shadows of Black Holes.- Time-domain inspiral templates for spinning compact binaries in quasi-circular orbits.