This reference and handbook describes theory, algorithms and applications of the Global Positioning System (GPS/Galileo). It is primarily based on source-code descriptions of the KSGsoft program developed by the author at the GFZ in Potsdam. The theory and algorithms are extended and verified for a new development of a multiple functional GPS/Galileo software. Besides the concepts such as the unified GPS data processing method and the numerical solution of the variation equations, as well as the general ambiguity search criteria reported in the first edition, there are several highlights reported. Such as the equivalent principle and its applications, the theory of independent parameterisation, the diagonalisation algorithm, etc. Mathematically rigorous, the book begins with the basics of coordinate and time systems and satellite orbits, as well as GPS observables, and deals with topics such as physical influences, observation equations and their parameterisation, adjustment and filtering, ambiguity resolution, data processing, and the determination of perturbed orbits.