This paper analyzes three-dimensional Yang-Mills and gravity theories with gauge-invariant mass terms. These theories, which are topologically nontrivial, significantly alter the particle content and lead to the quantization of a dimensionless mass-coupling-constant ratio. The vector field excitations become massive with spin 1, and the mass provides an infrared cutoff. Gravity acquires mass, mediates finite-range interactions, and has spin 2. The mass term, although third derivative in order, does not introduce ghosts or acausalities. The vector field action includes a Chern-Simons term, which changes the spin of the field from 0 to 1 and provides a perturbative infrared cutoff. The gravitational action includes a Chern-Simons term that transforms the Einstein action into a finite-range spin-2 field. The non-Abelian mass term has nontrivial homotopy properties, leading to the quantization of a dimensionless combination of mass and coupling constant. The equations of motion for the vector and gravitational fields are derived, showing that the excitations are massive. In linearized approximation, the right-hand sides of the equations are absent, indicating that all particles are massive with causal propagation. The linearized actions for Yang-Mills and gravity are expressed in terms of gauge-invariant components of the fields, showing that the vector theory has spin 1 and the gravitational theory has spin 2. The topological terms in the Lagrangians change under gauge transformations, leading to a quantization condition for the mass-coupling-constant ratio. The models are quantized, with the mass term acting as an infrared cutoff. In gravity, the conformal sector shows improved ultraviolet behavior, with the propagator decaying as $ p^{-3} $. The models are related to four-dimensional theories, with topological terms arising from the $ \theta $ vacuum of four-dimensional physics. The paper also discusses the external-source problem, showing that the effective Yukawa attraction in gravity contrasts with the interactions mediated by Einstein gravity. The vector theory also implies short-range source interactions, with the longitudinal electric field becoming short range. The results raise questions about the infrared properties of the vector model and the ultraviolet behavior of gravity and supergravity. The paper concludes that supergravity can be constructed and that the models have implications for energy positivity and the behavior of the metric at infinity.This paper analyzes three-dimensional Yang-Mills and gravity theories with gauge-invariant mass terms. These theories, which are topologically nontrivial, significantly alter the particle content and lead to the quantization of a dimensionless mass-coupling-constant ratio. The vector field excitations become massive with spin 1, and the mass provides an infrared cutoff. Gravity acquires mass, mediates finite-range interactions, and has spin 2. The mass term, although third derivative in order, does not introduce ghosts or acausalities. The vector field action includes a Chern-Simons term, which changes the spin of the field from 0 to 1 and provides a perturbative infrared cutoff. The gravitational action includes a Chern-Simons term that transforms the Einstein action into a finite-range spin-2 field. The non-Abelian mass term has nontrivial homotopy properties, leading to the quantization of a dimensionless combination of mass and coupling constant. The equations of motion for the vector and gravitational fields are derived, showing that the excitations are massive. In linearized approximation, the right-hand sides of the equations are absent, indicating that all particles are massive with causal propagation. The linearized actions for Yang-Mills and gravity are expressed in terms of gauge-invariant components of the fields, showing that the vector theory has spin 1 and the gravitational theory has spin 2. The topological terms in the Lagrangians change under gauge transformations, leading to a quantization condition for the mass-coupling-constant ratio. The models are quantized, with the mass term acting as an infrared cutoff. In gravity, the conformal sector shows improved ultraviolet behavior, with the propagator decaying as $ p^{-3} $. The models are related to four-dimensional theories, with topological terms arising from the $ \theta $ vacuum of four-dimensional physics. The paper also discusses the external-source problem, showing that the effective Yukawa attraction in gravity contrasts with the interactions mediated by Einstein gravity. The vector theory also implies short-range source interactions, with the longitudinal electric field becoming short range. The results raise questions about the infrared properties of the vector model and the ultraviolet behavior of gravity and supergravity. The paper concludes that supergravity can be constructed and that the models have implications for energy positivity and the behavior of the metric at infinity.