This text constitutes a documented study of the evolution of mathematics during the first half of the 20th century. Its list of primary sources and secondary publications adds to its value as a reference volume. It grew out of a colloquium organized by the Luxembourg Mathematical Society which was held at Chateau de Bourglinster in June 1992. The book's explicit chronology marks key events in the development of mathematics. One study by the late J. Dieudonne describes the history of topology; other important topics are covered in articles by J.L. Doob, G.Fichera, M. Guillaume, W. Hayman, C. Houzel, J.-P. Kahane, A. Lichnerowicz, J. Mawhin, L. Nirenberg, J.-P. Pier and W. Schwarz.