'The most incomprehensible thing about the world is that it is comprehensible.' ALBERT EINSTEIN, 1950 The tremendous progress of recent years in the field of isotopes in the earth sciences has proved invaluable in attempting to solve a varied spectrum of geological and geochemical problems. The lunar exploration programmes provided rocks for analysis, stimulating refinements in mass spectrometry which were later used for terrestrial samples too. Among significant advances was the development of electrostatic tandem accelerator mass spectrometers allowing the precise measure- ment of abundances of cosmic radionuclides. Also, new geochronometers were devised, for instance those dependent upon the radioactive decay of samarium-I47 to neodymium-I43, lutetium-176 to hafnium-176, rhenium-I87 to osmium-I87 and potassium-40 to calcium40, these supplementing prior dating methods. Their impact as regards the origin of igneous rocks was considerable. Isotopic compositions of neodymium, strontium, lead and hafnium in these rocks showed that magmas from the mantle are often crustally contaminated.In addition, isotopic compositions of carbon, oxygen and sulphur aided the elucidation of aspects of petrogenesis. These and many other facets of the subject are discussed in this book.