The mechanics of space flight is an old discipline. Its topic originally was the motion of planets, moons and other celestial bodies in gravitational fields. Kepler's (1571-1630) observations and measurements have led to probably the first mathematical description of planet's motion. Newton (1642-1727) gave then, with the development of his principles of mechanics, the physicalexplanation of these motions. Since then man has started in the second half of the 10th century to capture physically the Space in the sense that he did develop artificial celestial bodies, which he brought into Earth's orbits, like satellites or space stations, or which he did send to planets or moons of our planetary system, like probes, or by which people were brought to the moon and back, like capsules. Further he developed an advanced space transportation system, the U.S. Space Shuttle Orbiter, which is the only winged space vehicle ever in operation. Today it is no problem to solve the governing equations in the most general form using discrete numerical methods. The numerical approximation schemes, the computer power and the modern storage capacity are in such an advanced state, that solutions with high degree of accuracy can be obtained in a few seconds. Therefore the general practice in this book is to provide numerical solutions for all discussed topics and problems. This could be the orbit determination by the orbital elements, Lagrange's perturbation equations for disturbed Earth's orbits, the flight of a mass point in flight path coordinates (three degree of freedom), and the flight of a controlled space vehicle in body fixed coordinates (six degree of freedom). This book has been written not only for graduate and doctoral students but also for nonspecialists who may be interested in this subject or concerned with space flight mechanics.