In 1770, one of the founders of pure mathematics, Leonard Euler (1707-1783), published an algebra textbook for students. It was soon translated into French, with notes and additions by Joseph-Louis Lagrange, another giant of eighteenth-century mathematics, and the French edition was used as the basis of the English edition of 1822 (which also appears in this series), and of this 1790s German edition by Johann Philipp Gruson, Professor of Mathematics to the royal cadets. Volume 2 consists of two parts: 16 chapters on algebraic equations, followed by 15 chapters on analyses of indeterminate quantities. Here, Euler shows the reader several ways to solve polynomial equations up to the fourth degree. This landmark book showed students the beauty of mathematics, and more significantly, how to do it. It provides tangible evidence of the lively international mathematical community that flourished despite the political uncertainties of the late eighteenth century.