One of the eighteenth century’s greatest mathematicians, Lagrange made significant contributions to all fields of analysis and number theory. He survived the French Revolution to deliver these lectures in 1795 at the École Normale, a training school for teachers. An exemplar among elementary expositions, Lagrange’s talks feature both originality of thought and elegance of expression.The five lectures begin with discussions of arithmetic that focus on fractions and logarithms as well as theory and applications. Subsequent talks consider algebra, with emphasis on the resolution of equations of the third and fourth degree, the resolution of numerical equations, and the employment of curves in the solution of problems. Students, teachers, and others with an interest in mathematics will find this volume a unique reading book in mathematics, with fascinating historical and philosophical remarks by a distinguished mathematician.