  We develop the complete composite theory of gravity, in which the gauge
vector fields of the Yang-Mills theory with Lorentz symmetry group are
expressed in terms of the tetrad variables obtained from the decomposition of a
metric. A key element of a compelling formulation of composite gravity are
refined coordinate conditions that offer a natural coupling of the
gravitational field to matter and ensure the closest relationship to general
relativity. The composite theory of gravity is presented from three different
perspectives highlighting its intuitive interpretation, its relationship to
general relativity and its canonical Hamiltonian formulation, where the latter
clarifies the structure of the heavily constrained theory and provides the
starting point for its quantization. The main physical ingredient of the theory
is an anisotropic velocity-momentum relation, or tensorial mass, described by a
metric. We discuss the static isotropic solution in great detail because it
provides the background for the high-precision tests to be passed by an
alternative theory of gravity and for the understanding of black holes.
