This classic textbook is an introduction to the systematics and the use of stable isotopes in geosciences. It is subdivided into three parts: i) theoretical and experimental principles, ii) fractionation processes of light and heavy elements, iii) the natural variations of geologically important reservoirs. Since the publication of the previous edition improvements in multi-collector ICP mass-spectrometry have increased the ability to measure isotope ratios with very high precision for many elements of the periodic table. The amount of published data has increased tremendously in the last years; thus, conclusions based on a limited database are now better constrained. In this new edition, therefore, 47 elements with resolvable natural variations in isotope composition are discussed. This increase of elements, together with advances in the calculation of equilibrium isotope fractionation using ab initio methods, has led to an unbelievable rise of publications, making substantial major revisions and extensions of the last edition necessary. Many new references have been added, which enable quick access to recent literature.