Number Theory
Coursera
Four-week UC San Diego course building from division with remainder and modular arithmetic to Euclid's algorithm and RSA. Finishing it, you can encrypt and decrypt messages and break RSA implementations that reuse or mishandle keys.
More resources on Number Theory
Mathologer
Deep mathematical explorations covering number theory, geometry, combinatorics, and recreational mathematics with rigorous proofs.
numbertheory.org
Numbertheory.org is a comprehensive online hub for learning number theory, offering curated tutorials, lecture notes, bibliographies, and a wide collection of links to papers, software, and related resources.
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
primes.utm.edu
Primes.utm.edu, The Prime Pages, is a comprehensive number theory resource focused on primes, offering extensive prime catalogs (including Mersenne primes), historical notes, tables, and references to algorithms, software, and research data.
This Week's Finds in Mathematical Physics, Week 201
John Baez's 2004 expository column introducing Galois theory through symmetry: Galois groups of field extensions, quadratic and cyclotomic number fields, the fundamental theorem, why the quintic has no radical solution, and classical construction problems, with pointers toward class field theory.
Elementary Number Theory
Explore the beauty of numbers! This elementary number theory course covers divisibility, primes, congruences, and more.