TrinityCore uses (parts of or in whole) the following opensource software :

ACE (ADAPTIVE Communication Environment)
  http://www.cs.wustl.edu/~schmidt/ACE.html

bzip2 (a freely available, patent free, high-quality data compressor)
  http://www.bzip.org/

G3D (a commercial-grade C++ 3D engine available as Open Source (BSD License)
  http://g3d.sourceforge.net/

jemalloc (a general-purpose scalable concurrent malloc-implementation)
  http://www.canonware.com/jemalloc/

libMPQ (a library for reading MPQ files)
  https://libmpq.org/

MersenneTwister (a very fast random number generator)
  http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html

SFMT (SIMD-oriented Fast Mersenne Twister)
  http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/index.html

MySQL (the world's most popular open source database software)
  http://www.mysql.com/about/

OpenSSL (an opensource toolkit implementing SSL v2/v3 and TLS v1 protocols)
  http://www.openssl.org/

sockets (a GPL licensed C++ class library wrapping the berkeley sockets C API)
  http://www.alhem.net/Sockets/

utf8-cpp (UTF-8 with C++ in a Portable Way)
  http://utfcpp.sourceforge.net/

vld (a free open-source memory leak detection system for Visual C++)
  http://sites.google.com/site/dmoulding/vld

zlib (A Massively Spiffy Yet Delicately Unobtrusive Compression Library)
  http://www.zlib.net/