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Books about the Theory of Numbers

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• A Computational Introduction to Number Theory and Algebra

  http://shoup.net/ntb/
  By Victor Shoup (Cambridge University Press, 2005). Full text free in PDF, list of errata, supplementary exercises.

• A Friendly Introduction to Number Theory

  http://www.math.brown.edu/~jhs/frint.html
  J.H. Silverman. Contents, preface, errata, further material.

• Algorithmic Number Theory

  http://www.cs.uwaterloo.ca/~shallit/ant.html
  Eric Bach and Jeffrey Shallit. Errata, bibliography in BibTeX format.

• Analytic Number Theory and Applications

  http://wain.mi.ras.ru/mian218.htm
  To Prof. Anatolii Alexeevich Karatsuba on the occasion of his 60th birthday. A collection of papers in DVI and PostScript format.

• Automorphic Forms and Representations

  http://math.stanford.edu/~bump/book.html
  Dan Bump. Errata, contents, virtual study group.

• Collected Papers of Sarvadaman Chowla

  http://www.canisius.edu/~huard/chowla.html
  Edited by James G. Huard and Kenneth S. Williams. Contents.

• Discovering Number Theory

  http://math.la.asu.edu/~jj/dnt/
  A textbook by John Jones and Jeff Holt.

• eBooks in Number Theory

  http://fs.gallup.unm.edu/ebooks-otherformats.htm
  Mainly connected with Smarandache problems. PDF, HTML, WORD, WP, TeXT formats.

• Elliptic Curves: Number Theory and Cryptography

  http://www.math.umd.edu/~lcw/ec.html
  By Larry Washington (Chapman+Hall/CRC, 2003). Contents, errata.

• Factorizations of b^n+/-1

  http://www.ams.org/online_bks/conm22/
  b=2,3,5,6,7,10,11,12 Up to High Powers.By John Brillhart, D.H. Lehmer, J.L. Selfridge, Bryant Tuckerman and S.S. Wagstaff, Jr. Third edition, AMS, 2002. Complete text available for free download in PDF.

• Fundamental Number Theory with Applications

  http://people.ucalgary.ca/~ramollin/fnt2.html
  Richard A. Mollin. Contents.

• Gauss and Jacobi Sums

  http://math.ucsd.edu/~revans/errata/errata.html
  Bruce C. Berndt, Ronald J. Evans, and Kenneth S. Williams (Wiley, 1998). Contents, errata, remarks, reviews.

• Introduction to Cyclotomic Fields

  http://www.math.umd.edu/~lcw/cyclo.html
  2nd ed. by Larry Washington (Springer). Errata.

• Local Fields and Their Extensions, Second Edition

  http://www.maths.nottingham.ac.uk/personal/ibf/book/book.html
  I.B. Fesenko, S.V. Vostokov. PDF files.

• Paul Garrett's Crypto and Number Theory Lecture Notes

  http://www.math.umn.edu/~garrett/crypto/
  Introduction to cryptology, number-theory, and algorithms. Protocols. Symmetric versus asymmetric systems. Stream, block ciphers. One-way functions, signatures. Key management. (Pseudo-) random number generation. Permutation groups. Primes, Euclidean algorithm. Finite fields. Quadratic reciprocity. Discrete logs, RSA. Pseudoprimes, rho method. Elliptic curve methods.

• Primes of the Form x^2 + ny^2

  http://www.cs.amherst.edu/~dac/primes.html
  By David A. Cox, Amherst College (Wiley, 1989). Errata.

• Reciprocity Laws from Euler to Eisenstein

  http://www.rzuser.uni-heidelberg.de/~hb3/rec.html
  Franz Lemmermeyer (Springer, 2000). Contents, bibliography, errata.

• Sphere Packing, Lattices and Groups

  http://neilsloane.com/doc/splag.html
  J. H. Conway and N. J. A. Sloane (Springer, 1998). Contents, errata (including a missing page), updated tables and database.

• Taming Wild Extensions

  http://math.albany.edu:8000/~lc802/mono.html
  By Lindsay N. Childs. Introduction.

• The Third Edition of the Cunningham Book

  http://www.cerias.purdue.edu/homes/ssw/cun/third/
  Factorizations of bn ± 1, b = 2, 3, 5, 6, 7, 10, 11, 12, up to High Powers, by John Brillhart, D.H. Lehmer, J.L. Selfridge, Bryant Tuckerman, and S.S. Wagstaff, Jr. An electronic book: links to full text [PDF] and tables.

• Voronoi's Impact on Modern Science

  http://www.imath.kiev.ua/~syta/vorbook.html
  Edited by P.Engel and H.Syta. Contents, ordering information.

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