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Number Theory A Contemporary Introduction
This note describes the following topics: Pythagorean Triples, Quadratic Rings, Quadratic Reciprocity, The Mordell Equation, The Pell Equation, Arithmetic Functions, Asymptotics of Arithmetic Functions, The Primes: Infinitude, Density and Substance, The Prime Number Theorem and the Riemann Hypothesis, The Gauss Circle Problem and the Lattice Point Enumerator, Minkowski’s Convex Body Theorem, The Chevalley-Warning Theorem, Dirichlet’s Theorem on Primes in Arithmetic Progressions, Rational Quadratic Forms and the Local-Global Principle.
Author(s): Pete L. Clark
272 Pages 
Algebraic Number Theory by Dietrich Burde
This note explains the following topics: Integral ring extensions, Ideals of Dedekind rings, Finiteness of the class number, Dirichlets unit theorem, Splitting and ramification, Cyclotomic fields, Valuations and local fields, The theorem of Kronecker weber.
Author(s): Dietrich Burde
101 Pages
Number Theory by Lars Ake Lindahl
This PDF covers the following topics related to Number Theory : Divisibility, Prime Numbers, The Linear Diophantine Equation , Congruences, Linear Congruences, The Chinese Remainder Theorem, Public-Key Cryptography, Pseudoprimes, Polynomial Congruences with Prime Moduli, Polynomial Congruences with Prime Power Moduli, The Congruence, General Quadratic Congruences, The Legendre Symbol and Gauss’ Lemma, Quadratic Reciprocity, Primitive Roots, Arithmetic Functions, Sums of Squares, Pythagorean Triples, Fermat’s Last Theorem, Continued Fractions, Simple Continued Fractions, Rational Approximations to Irrational Numbers, Periodic Continued Fractions, Continued Fraction Expansion, Pell’s Equation.
Author(s): Lars Ake Lindahl
95 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
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