This volume contains the two most important essays on the logical foundations of the number system by the famous German mathematician J.W.R. Dedekind. The contents of these essays belong to the foundations of mathematics, and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the members of our number system. As a major work of an important mathematician and every teacher and historian of mathematics. 1963 republication of original 1901 translation from the German