Preface. 1: Prologue to the History of the IMU. 2: The Old IMU (1920- 1932). 3: Mathematical Cooperation Without the IMU (1933-1939). 4: Foundation of the New IMU (1945-1951). 5: The IMU Takes Shape (1952- 1954). 6: Expansion of the IMU (1955-1958). 7: The IMU and International Congresses (1958-1962). 8: Consolidation of the IMU (1963-1970). 9: North-South and East-West Connections (1971-1978). 10: Politics Interferes with the IMU (1979-1986). 11: The IMU and Related Organizations. 12: The IMU in a Changing World (1986-1990). Appendix.