Part I. The theory of time-independent accretion disks around compact objects is developed, generalizing the stationary models of various authors to allow time dependence on the radial-flow time scale. Equations are derived for the time evolution of matter surface density [Sigma] and for implicit expressions of relevant disk variables in terms of [Sigma]. Analytic and numerical studies of these equations yield numerical models of mass accretion from a disk onto a compact object and a discovery of the unstable nature of the "inner region" of the disk, causing a breakdown of current accretion disk models. Part II. Theoretical frameworks for analyzing and testing gravitation theories are developed for both nonmetric and metric theories. Highly precise experimental confirmation of the Weak Equivalence Principle is shown to be deadly if not fatal evidence for ruling out all nonmetric theories of gravity. For the class of metric theories we demonstrate the necessity for going beyond current frameworks of analysis (e.g.,the PPN framework) by constructing a new theory of gravity identical to GRT in the Post-Newtonian limit. As a first step in transcending current frameworks, we develop a formalism for delineating and testing all metric theories of gravity on the basis of their gravitational-wave properties and thereby emphasize gravitational-wave observations as a future tool for testing gravitation theories. We also investigate conservation laws and some common properties of Lagrangian-based metric theories of gravity.