This volume traces the transformation of the United States from a mathematical backwater to a major presence during the quarter-century from 1876 to 1900. Presenting a detailed study of the major figures involved in this transformation, it focuses on the three most influential individuals—the British algebraist James Joseph Sylvester, the German standard-bearer Felix Klein, and the American mathematician Eliakim Hastings Moore—and on the principal institutions with which they were associated—the Johns Hopkins University, Göttingen University, and the University of Chicago. This book further analyzes the research traditions these men and their institutions represented, the impact they had on the second generation of American mathematical researchers, and the role of the American Mathematical Society in these developments. This is the first work ever written on the history of American mathematics during this period and one of the few books that examines the historical development of American mathematics from a wide perspective. By placing the development of American mathematics within the context of broader external factors affecting historical events, the authors show how the character of American research was decisively affected by the surrounding scientific, educational, and social contexts of the period. Aimed at a general mathematical audience and at historians of science, this book contains an abundance of unpublished archival material, numerous rare photographs, and an extensive bibliography.