Owing to the increased accuracy requirements in fields such as astrometry and geodesy the general theory of relativity must be taken into account for any mission requiring highly accurate orbit information and for practically all observation and measurement techniques. This book highlights the confluence of Applied Mathematics, Physics and Space Science as seen from Einsteins general theory of relativity and aims to bridge the gap between theoretical and applied domains. The book investigates three distinct areas of general relativity: Exact solutions of the Einstein field equations of gravitation. Dynamics of near-Earth objects and solar system bodies. Relativistic orbitography. This book is an updated and expanded version of the author PhD thesis which was awarded the International Astronomical Union PhD prize in Division A: Fundamental Astronomy. Included is a new introduction aimed at graduatestudents of General Relativity and extended discussions and results on topics in post-Newtonian dynamics and general relativistic spacecraft propagation.