Geometrical methods for kinematics and dynamics in relativistic theories of gravity with applications to cosmology and space physics The main goal of this work is to estimate the effect of the global cosmological expansion of the Universe on the dynamics of local systems and on measurements. Examples are the motion of planets and spacecrafts and their Doppler tracking. For this purpose we first develop a general framework for relativistic kinematics and dynamics within which these problems can be precisely formulated and solved. In the next step we discuss in detail in the setting of General Relativity appropriate models for quasi isolated structures in a cosmological spacetime. Here we specialize on spherically symmetric spacetimes and make use of their rich geometrical structure which allows in particular to construct useful quasi local mass concepts...