This work represents the co-operation of many specialists on a single, very complex problem. I am not in any sense an archæologist, and in this important and highly technical field I have relied chiefly upon the work of Hugo Obermaier and of Déchelette in the Lower Palæolithic, and of Henri Breuil in the Upper Palæolithic. Through the courtesy of Doctor Obermaier I had the privilege of watching the exploration of the wonderful grotto of Castillo, in northern Spain, which affords a unique and almost complete sequence of the industries of the entire Old Stone Age. This visit and that to the cavern of Altamira, with its wonderful frescoed ceiling, were in themselves a liberal education in the prehistory of man. With the Abbé Breuil I visited all the old camping stations of Upper Palæolithic times in Dordogne and noted with wonder and admiration his detection of all the fine gradations of invention which separate the flint-makers of that period. With Professor Cartailhac I enjoyed a broad survey of the Lower and Upper Palæolithic stations and caverns of the Pyrenees region and took note of his learned and spirited comments. Here also we had the privilege of being with the party who entered for the first time the cavern of Tuc d'Audoubert, with the Comte de Bégouen and his sons. In the American Museum I have been greatly aided by Mr. Nels C. Nelson, who has reviewed all the archæological notes and greatly assisted me in the classification of the flint and bone implements which is adopted in this volume. In the study of the divisions, duration, and fluctuations of climate during the Old Stone Age I have been assisted chiefly by Doctor Chester A. Reeds, a geologist of the American Museum, who devoted two months to bringing together in a comprehensive and intelligible form the results of the great researches of Albrecht Penck and Eduard Brückner embraced in the three-volume work, _Die Alpen im Eiszeitalter_. The temperatures and snow-levels of the Glacial Epoch, which is contemporaneous with the Old Stone Age, together with the successive phases of mammalian life which they conditioned, afford the firm basis of our chronology; that is, we must reckon the grand divisions of past time in terms of Glacial and Interglacial Stages; the subdivisions are recorded in terms of the human invention and progress of the flint industry. I have also had frequent recourse to _The Great Ice Age_ and the more recent _Antiquity of Man in Europe_ of James Geikie, the founder of the modern theory of the multiple Ice Age in Europe.