The author divides the century between 1776 and 1876 into the following three “generations”: 1776–1800 the post-colonial generation, 1800–1838 the Bowditch generation, 1838–1876 the Benjamin Peirce generation. In his book the first two generations are analyzed in detail. The author describes all the scientific and mathematical journals which were founded during this epoch; in 1804 the first volume of “The Mathematical Correspondent” appeared, in 1808 “The Analyst, or Mathematical Museum”. Most of them did not survive for a longer period. During the years from 1636 to 1769 in total 9 colleges were founded. In 1802 the foundation of the Military Academy in Westpoint followed, an institution, similar to the École Polytechnique, where students intended to become engineers. Many textbooks of this time were translations, mostly from the French; so John Farrar, professor in Harvard, translated Euler, Legendre, Bézout. In 1814, a first textbook in algebra written by an American author was published: Jeremiah Day, An introduction to algebra; there were 67 editions! Nathaniel Bowditch, who never was professor of mathematics, was of greatest influence; his first publication, New American practical navigator, appeared first in 1799; there was a second edition and many reprints. Bowditch’s translation of Laplace’s Mécanique céleste into English (4 vols., Boston 1829–1839) was a milestone in the history of American mathematics. The author concludes: “Nathaniel Bowditch left a lasting legacy on American mathematics, astronomy and science in general” (p. 126). It was Bowditch who encouraged and guided Benjamin Peirce, the main mathematician of the third generation. There is a bibliography (pp. 217–230) and there are four appendices: A) “Mathematical content of American journals, 1771–1834”; B) “Contributions to American mathematics journals”; C) “American mathematicians published in major American science journals 1771–1834”; D) “John Farrar’s Cambrige course of mathematics”. It is astonishing that among the American mathematicians who published in American journals also Europeans like John Bradley, David Brewster and J. J. Littrow are mentioned. The book is a very important contribution to the history of mathematics in America. It precedes [K. H. Parshall and D. E. Rowe, The emergence of the American mathematical research community, 1876–1900: J. J. Sylvester, Felix Klein, and E. H. Moore. Providence, RI: American Mathematical Society; London: London Mathematical Society (1994; Zbl 0802.01005)].