[For the review of the German reprint (1983), cf. Zbl 0521.01031.]
Euler’s introductio in analysin infinitorum (1748) is a textbook on algebra and geometry which provides the reader with the necessary groundwork for study of his textbooks on the calculus, Institutiones calculi differentialis (1755) and Institutiones calculi integralis (1768- 1770). Introduction to analysis of the infinite, Book I, is a translation of the volume of Euler’s textbook that deals with algebra. It covers what would now be described as advanced algebra and includes a treatment of elementary algebraic, trigonometric, exponential and logarithmic functions and their expansions in infinite series. The exposition is, of course, very clear, and the translation could easily be mistaken for a modern textbook suitable for the higher classes in secondary schools and students beginning a university course in mathematics.