This monograph has grown from my PhD thesis Interior point Methods for Semidefinite Programming [39] which was published in December 1997. Since that time, Semidefinite Programming (SDP) has remained a popular research topic and the associated body of literature has grown considerably. As SDP has proved such a useful tool in many applications, like systems and control theory and combinatorial optimization, there is a growing number of people who would like to learn more about this field.