This is the first truly comprehensive and thorough history of the development of mathematics in the United States and Canada. This first volume of a two-volume work takes the reader from the European encounters with North America in the fifteenth century up to the emergence of the United States as a world leader in mathematics in the 1930s. In the story of the Colonial period particular emphasis is given to several prominent Colonial figures--Jefferson, Franklin, and Rittenhouse-and four important early colleges-Quebec, Harvard, Yale, and William & Mary. During the first three-quarters of the nineteenth century, mathematics in North America was largely the occupation of scattered individual pioneers: Bowditch, Farrar, Adrain, B. Peirce. This period is given a fuller treatment here than previously in the literature, including the creation of the first PhD programs and attempts to form organizations and found journals. With the founding of Johns Hopkins University in 1876, the American mathematical research community was finally, and firmly, founded. The programs at Hopkins, Chicago, and Clark are detailed as are the influence of major European mathematicians, including especially Klein, Hilbert, and Sylvester. Extensive histories of early areas of American emphasis are provided, including axiomatics, topology, and group theory. Also included are the early histories of statistics and cryptology in America, laying the foundation for the latter topic's role in abstract algebra in the 1950s. The stories of both the American Mathematical Society and the Mathematical Association of America are presented in detail. David Zitarelli is emeritus Professor of Mathematics at Temple University. A decorated and acclaimed teacher, scholar, and expositor, he is one of the world's leading experts on the development of American mathematics. Author or co-author of over a dozen books, this is his magnum opus--sure to become the leading reference on the topic and essential reading, not just for historians. In clear and compelling prose, Zitarelli spins a tale accessible to experts, generalists, and anyone interested in the history of science in North America.