thank Professor Beiglbock for suggestions he made to improve Part lIon Spaces of Constant Curvature, and Drs. S. and J. Mitton for translating the manuscript into English. I also thank with pleasure Marie-Ange Sevin for correcting the final version. J. Heidmann March 1980, Meudon, France Preface The aim of this book is to present the fundamentals of cosmology. Its subject is the study of the universe on a grand scale: - on a grand distance scale, since from the start, we shall be escaping the con­ fines of our own Galaxy to explore space as far as the limits of the observable universe, some ten thousand million light years away; - and on a grand time scale, as we shall look back into the past to the very first moments of the initial expansion, about twelve thousand million years ago.