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The Theory of Numbers
Robert Daniel Carmichael (March 1, 1879 – May 2, 1967) was a leading American mathematician.The purpose of this little book is to give the reader a convenient introduction to the theory of numbers, one of the most extensive and most elegant disciplines in the whole body of mathematics. The arrangement of the material is as follows: The five chapters are devoted to the development of those elements which are essential to any study of the subject. The sixth and last chapter is intended to give the reader some indication of the direction of further study with a brief account of the nature of the material in each of the topics suggested.
Author(s): R. D. Carmichael
88 Pages 
Number Theory Lecture Notes by Vahagn Aslanyan
This note explains the following topics: Divisibility, Multiplicative functions, Modular arithmetic, Primitive roots, Quadratic residues, Diophantine equations, Quadratic number fields, Chebyshev’s theorem.
Author(s): Vahagn Aslanyan
69 Pages
Analytic Number Theory Lecture Notes by Andreas Strombergsson
This note covers the following topics: Primes in Arithmetic Progressions, Infinite products, Partial summation and Dirichlet series, Dirichlet characters, L(1, x) and class numbers, The distribution of the primes, The prime number theorem, The functional equation, The prime number theorem for Arithmetic Progressions, Siegel’s Theorem, The Polya-Vinogradov Inequality, Sums of three primes, The Large Sieve, Bombieri’s Theorem.
Author(s): Andreas Strombergsson
295 Pages
Theory of Numbers Lecture Notes
This lecture note is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.
Author(s): Prof. Abhinav Kumar
NA Pages
An Introductory Course in Elementary Number Theory
The notes contain a useful introduction to important topics that need to be addressed in a course in number theory. Proofs of basic theorems are presented in an interesting and comprehensive way that can be read and understood even by non-majors with the exception in the last three chapters where a background in analysis, measure theory and abstract algebra is required.
Author(s): Wissam Raji
171 Pages
A Course on Number Theory (PDF 139P)
This note explains the following topics: Algebraic numbers, Finite continued fractions, Infinite continued fractions, Periodic continued fractions, Lagrange and Pell, Euler’s totient function, Quadratic residues and non-residues, Sums of squares and Quadratic forms.
Author(s): Peter J. Cameron
139 Pages
Lectures on Topics in Algebraic Number Theory (PDF 83P)
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Automorphic Forms, Representations, and L Functions
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A Course In Algebraic Number Theory
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Number theory and elementary arithmetic
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An Introduction to the Theory of Numbers
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An Introduction to p adic Numbers and p adic Analysis (PDF 64p)
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