"Physical Geodesy" by Heiskanen and Moritz, published in 1967, has for a long time been considered as the standard introduction to its field. The enormous progress since then, however, required a complete reworking. While basic material could be retained other parts required a complete update. This concerns, above all, the adaptation to the fact that the geometry can now be precisely determined by methods such as GPS, and that new satellite methods, combined with terrestrial methods, also make a detailed determination of the earth's gravitational field a possibility and a necessity. Highlights include: emphasis on global integration of geometry and gravity, a simplified approach to Molodensky's theory without integral equations, and a general combination of all geodetic data by least-squares collocation. In the second edition minor mistakes have been corrected.