An Introductory Course in Elementary Number TheoryWissam RajiPDF  171 Pages  EnglishThe
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
nonmajors with the exception in the last three chapters where a background in
analysis, measure theory and abstract algebra is required.

Elementary Number Theory Primes, Congruences, and SecretsWilliam SteinOnline  NA Pages  EnglishThis is a
textbook about classical elementary number theory and elliptic curves. The first
part discusses elementary topics such as primes, factorization, continued
fractions, and quadratic forms, in the context of cryptography, computation, and
deep open research problems. The second part is about elliptic curves, their
applications to algorithmic problems, and their connections with problems in
number theory.

Algebraic Number Theory by Paul GarrettPaul GarrettOnline  NA Pages  EnglishThis note contains the
following subtopics: Classfield theory, homological formulation, harmonic
polynomial multiples of Gaussians, Fourier transform, Fourier inversion on
archimedean and padic completions, commutative algebra: integral extensions
and algebraic integers, factorization of some Dedekind zeta functions into
Dirichlet Lfunctions, meromorphic continuation and functional equation of zeta,
Poisson summation and functional equation of theta, integral representation of
zeta in terms of theta.

The Theory of NumbersR. D. CarmichaelOnline  88 Pages  EnglishRobert 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.

An Introduction to Algebraic Number TheoryFrederique
OggierOnline  NA Pages  EnglishThis note covers the following topics: Algebraic numbers and algebraic
integers, Ideals, Ramification theory, Ideal class group and units, padic
numbers, Valuations, padic fields.

Number TheoryFermats Last Theorem (PDF 18P)Reinhard Laubenbacher and
David PengelleyPDF  18 Pages  EnglishThis note covers the
following topics: Fermat’s Last Theorem , Euclid's Classification of Pythagorean Triples and
Germain's General Approach.

A Course on Number Theory (PDF 139P)Peter J. CameronPDF  139 Pages  EnglishThis
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 nonresidues, Sums of squares and Quadratic forms.

Lectures on Topics in Algebraic Number Theory (PDF 83P) 
Notes on Number Theory (PDF 58P) 
A Modern Course on Curves and Surfaces 
Introduction to Algebraic Number Theory 
Introduction to Number Theory 
ALGEBRAIC NUMBER THEORY 
Automorphic Forms, Representations, and L Functions 
Elementary Number Theory ebook 
A Computational Introduction to Number Theory 
Analytic Number Theory 
A Course In Algebraic Number Theory 
Algorithmic Number Theory 
Number theory and elementary arithmetic 
Algebraic Number Theory Course Notes 
Combinatorial and Analytic Number Theory 
Computational Number Theory 
Number Theory and Cryptography 
Algebra and Number Theory 
Algebraic Number Theory summary of notes 
The ABCs of Number Theory 
Elementary Number Theory Chen W.W.L 
Elementary Number Theory Clark W.E. 
An Introduction to the Theory of Numbers 
Introduction to Number Theory (PDF 25P) 
An Introduction to p adic Numbers and p adic Analysis (PDF 64p) 
Algebra and Number Theory (PDF 64p) 
Modular forms 