Some books/course notes:

• Bernd Gaertner and Jiri Matousek's book on Approximation Algorithms and Semidefinite Programming.
• Yinyu Ye's lecture notes on Linear Conic Optimization.
• Carsten Scherer and Siep Weiland's notes on linear matrix inequalities in control.
• David Williamson's notes on approximation algorithms , including SDP approaches for combinatorial optimization.
• Denis Arzelier and Didier Henrion's lecture notes on LMI optimization and applications (this page is French, but the notes aren't!). See in particular the section on Relaxations LMI.
• Lieven Vandenberghe and Steve Boyd's SIAM Review paper on SDP.
• Anthony So and Yinyu Ye's paper on SDP relaxations for sensor localization.
• The Goemans-Williamson paper on MAXCUT.
• Laszlo Lovasz's Shannon capacity paper.
• Don Knuth's survey paper on Lovasz's sandwich theorem for $\vartheta$.
• Alper Yildirim and Xiaofei Fan-Orzechowski's paper on using the Lovasz theta function to extract a maximum stable set for perfect graphs.
• Michel Goemans's survey paper on SDP in combinatorial optimization.
• Pablo Parrilo's paper on SDP approaches to semialgebraic (polynomial optimization) problems.
• Renato Monteiro's paper on methods for solving SDPs.
• Christoph Helmberg's and Franz Rendl's paper on spectral bundle methods for SDP.
• My paper on potential-reduction algorithms, mostly for linear programming but Section 8 deals with extensions including SDP.
  There are also chapters on applications and path-following and potential-reduction methods in
• The Handbook on Semidefinite Programming, online here, and that on semidefinite, conic, and polynomial programming here.
• Some useful references are here.
• And here is a bibliography on SDP compiled by Henry Wolkowicz.

Useful sites

• Home pages on SDP: Christoph Helmberg's and Farid Alizadeh's. Both have links to papers and software; the second is very much out of date, but can also be helpful.
• A useful page from Henry Wolkowicz.
• The Interior-Point Methods Online and Optimization Online archives.
• The software package SDPT3.
• Some benchmark results by Hans Mittelmann can be found here.
• The DIMACS challenge on SDP and results of some codes.