Semidefinite programming (SDP) is one of the research areas in optimization. It has and continues to attract researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This research activity has been prompted by the discovery of applications in combinatorial optimization and control theory, the development of efficient interior-point algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory. This handbook offers an advanced and broad overview of the field. It contains 19 chapters organized in three parts: theory, algorithms, and applications and extensions.