Online number theory lecture notes and teaching materials

  1. Number Theory - Summer School aimed at undergraduate students Lisbon, July 11-15, 2011
  1. Online Math Courses, videos and lectures from leading universities. This has links to some excellent number theory courses.
  2. Algebraic Number Theory and commutative algebra, lecture notes by Robert Ash
  3. lecture notes on p-adic numbers and introductory number theory (Andrew Baker)
  4. Algebraic number theory notes (Matt Baker - pdf)
  5. An exposition of the elementary proof of the prime number theorem of Atle Selberg (Simone Battagliero)
  6. Cours d'arithmétique, notes by Pascal Boyer
  7. Zahlentheorie (Notes by Winfried Bruns)
  8. L-functions (lecture course by Kevin Buzzard)
  9. A course in number theory (Peter Cameron)
  10. Algebraic Number Theory and Automorphic L-functions, lecture notes by Ching-Li Chai
  11. A Course on Number Theory (Peter J. Cameron)
  12. Curso avanzado de Teoría de Números (Fernando Chamizo)
  13. Algebraic Number Theory I (Pete L. Clark)
  14. Computational class field theory, A course given at the Middle East Technical University, Ankara, 1997 by Henri Cohen (dvi 255K)
  15. Draft chapters of elliptic curve handbook ECH1 (Ian G. Connell)
  16. Modular forms (draft, CTNT 2016) (Keith Conrad) Lectures
  17. Lecture notes for Math 259: Introduction to Analytic Number Theory (Spring 1998) (Noam Elkies)
  18. Math 780: Elementary Number Theory, Notes by Michael Filaseta, 1997
  19. lectures on cryptography, Heraklion, Crete 2003, (Gerhard Frey)
  20. Vinogradov's three-primes theorem, notes by Timothy Gowers (dvi 54K)
  21. Fall 2012-Math 201 Elementary Number Theory, Aaron Greicius
  22. Curves over finite fields, Richard Griffon
  23. Elementary Number Theory, by Peter Hackman
  24. Azar y Aritmética (a course on probabilistic number theory by Harald Helfgott)
  25. lecture notes on elementary number theory (Bruce Ikenaga)
  26. Number Theory lecture notes (Eugen Ionascu)
  27. Math 254B (Number Theory), lecture notes on class field theory, abelian extensions of number fields etc (Kiran Kedlaya)
  28. Notes on class field theory, Kiran S. Kedlaya
  29. 18.785: Analytic Number Theory (MIT, Spring 2007, Kiran Kedlaya)
  30. Cours de cryptographie, notes by Alain Kraus
  31. Algebraic Number Theory, lecture Notes by Franz Lemmermeyer
  32. Quadratische Zahlkörper, lecture notes by Franz Lemmermeyer
  33. Topics in Algebraic Geometry: Elliptic Curves, lecture course by Franz Lemmermeyer
  34. Number theory lecture notes from Leiden University
  35. Exploring Number Theory, a blog on elementary number theory by Dan Ma
  36. Course notes in elementary number theory by Rudolph Maier (in Portuguese)
  37. Introduction to number theory (MATH 4803/5803), lecture notes by Kimball Martin
  38. Number theory ii (MATH 6393), lecture notes on algebraic number theory by Kimball Martin
  39. Modular forms (MATH 6393), lecture notes by Kimball Martin
  40. Theory of Numbers, lecture notes by Yotsanan Meemark
  41. Course Notes by Jim Milne: Algebraic number theory, Class field theory, Algebraic Geometry, Elliptic Curves, Modular functions and forms, Abelian varieties, Etale Cohomology
  42. DEA 2003/04: Elliptic functions and elliptic curves, lecture notes by Jan Nekovář
  43. Part III Modular Forms, Lent 2014 (James Newton)
  44. Maple Tutorial for Number Theory (Don Rideout)
  45. Math 617-618 (graduate number theory), lecture notes by Yiannis Sakellaridis and Murilo Corato Zanarella
  46. Number Theory for Mathematical Contests (David Santos)
  47. Draft of PCMI lecture Notes on Open Questions in Arithmetic Algebraic Geometry (Alice Silverberg) (ps file 803K)
  48. Continued fractions, Pell's equation, generating functions (Joe Silverman)
  49. Chapters 1-6 of A friendly introduction to number theory by Joe Silverman
  50. Notes on additive combinatorics K. Soundararajan
  51. Notes by Jeff Hoffstein from a course Ma253 taught by Harold Stark at MIT
  52. Elementary Number Theory: Primes, Congruences, and Secrets, William Stein, Undergraduate Text, Springer 2009 (freely available online)
  53. Algebraic number theory course book (William Stein)
  54. lectures on Modular Forms and Hecke Operators (Ken Ribet and William A. Stein)
  55. Number rings, local fields, elliptic curves, lecture notes by Peter Stevenhagen
  56. Course notes on analytic number theory, algebraic number theory, linear forms in logarithms and diophantine equations (Cameron Stewart)
  57. Elliptische Kurven I/II, (lecture notes in German by Michael Stoll)
  58. Introductory Number Theory (Course notes by Michael Stoll)
  59. Descent on Elliptic Curves (Course notes by Michael Stoll)
  60. Exercises on binary quadratic forms to supplement David Cox's book Primes of the Form x2+ny2 (Jeff Stopple)
  61. 18.785 Number Theory I (MIT, Fall 2019) (Andrew Sutherland)
  62. 18.783 Elliptic Curves (MIT, Spring 2019) (Andrew Sutherland)
  63. Combinatorial and Analytic Number Theory, (Robert Tijdeman 2007)
  64. Course notes in number theory (Felipe Voloch)
  65. Introduction to Diophantine methods: irrationality and transcendence, course notes by Michel Waldschmidt
  66. Cours de théorie des nombres, notes by Michel Waldschmidt
  67. Algebraic number theory course notes (Tom Weston)
  68. Notes on elementary number theory (David Wilkins)
  69. Vorlesungsmanuskripte und Übungen zur Zahlentheorie (Dieter Wolke)
  70. Circulants, an online book by Alun Wyn-Jones
  71. Introduzione alla Teoria Analitica dei Numeri, lecture notes by Alessandro Zaccagnini

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Last modified 22nd October 2026