The main idea of this book is, on the grounds of the differential-geometric structures of the (Ln, g)-spaces and the kinematics of vector fields to set the stage for the study of physical and gravitational physical interactions. In order to accomplish this task, the book is divided into three parts. Part One briefly reviews and introduces the problems of theoretical gravitational physics. Part Two deals with the theory of differentiable manifolds with contravariant affine connections and metrics. Part Three investigates the kinematics of vector fields over (Ln, g)-spaces.