33 Number Theory
An Introduction to the Theory of Numbers 
Leo Moser
2004
Licence: CC BY
This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text.
Format: PDF
Suggested for: MATH 409
Number Theory: In Context and Interactive
Karl-Dieter Crisman (Gordon College)
2021
Licence: CC BY-NC
The book tackles all standard topics of modular arithmetic, congruences, and prime numbers, including quadratic reciprocity. In addition, there is significant coverage of various cryptographic issues, geometric connections, arithmetic functions, and basic analytic number theory, ending with a beginner’s introduction to the Riemann Hypothesis. Ordinarily this should be enough material for a semester course with no prerequisites other than a proof-transition experience and vaguely remembering some calculus.
Format: Online
