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 Many real-world applications, although being non-linear, can be well described by 
 linearized models. Therefore, Linear Programming (LP) became a widely studied and 
  applied technique in many areas of science, industry and economy. Semidefinite   
 Programming (SDP) is an extension of LP. A matrix-variable is optimized over the  
 intersection of the cone of positive semidefinite matrices with an affine space.  
 It turned out, that SDP can provide significantly stronger practical results than 
  LP. Since then SDP turned out to be practical in a lot of different areas, like  
   combinatorial optimization, control theory, engineering, and more recently in   
  polynomial optimization. \\ Due to the numerous areas of applications, solving   
 SDPs became a widely studied subject. Interior-Point Methods are the most popular 
algorithms nowadays. Recently, bundle methods and applying an augmented Lagrangian 
 algorithm have been used for solving SDPs. \\ In this talk I will state the basic 
  concept of SDP. I will show how to apply SDP to approximate the max-cut problem  
  and the coloring problem, two combinatorial optimization problems. Via the SDP   
  relaxations of these two combinatorial optimization problems I will explain the  
 methods for solving SDPs, in particular the recently developed bundle method for  
     max-cut and the boundary point method to compute the Lovasz theta-number.     
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