Two most important essays by the famous German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, thereby a rigorous meaning of continuity in analysis. The other is an attempt to give logical basis for transfinite numbers and properties of the natural numbers.
Here's a sample of other books in this Dover category
Number Theory by George E. Andrews Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more
The Number System by H. A. Thurston This book explores arithmetic's underlying concepts and their logical development, in addition to a detailed, systematic construction of the number systems of rational, real, and complex numbers. 1956 edition.
History of the Theory of Numbers, Volume I: Divisibility and Primality by Leonard Eugene Dickson Written by a Univeristy of Chicago professor, this 1st volume in the 3-volume series History of the Theory of Numbers presents the material related to the subjects of divisibility and primality. 1919 edition.
The Method of Trigonometrical Sums in the Theory of Numbers by I. M. Vinogradov This text investigates Waring's problem, approximation by fractional parts of the values of a polynomial, estimates for Weyl sums, distribution of fractional parts of polynomial values, Goldbach's problem, more. 1954 edition.
