A classic textbook, encompassing the analytical methods of classical celestial mechanics, numerical experiments on the orbital evolution of gravitating masses, and the astrodynamics of artificial satellites and interplanetary probes. The text requires little or no prior familiarity with astronomy or space science, but assumes a knowledge of calculus and elementary vector analysis. Problems, with answers, are included as are appendices of relevant astronomical and mathematical data. Intended primarily for postgraduate and advanced undergraduate students, but parts of the text can be used in more introductory courses and the discussion of orbital computation will be of interest to serious amateur astronomers.