Homological Projective Duality is a homological extension of the classical no- tion of projective duality. Constructing the homological projective dual of a variety allows one to describe semiorthogonal decompositions on the bounded derived cat- egory of coherent sheaves for all the complete linear sections of the initial variety. This gives a powerful method to construct decompositions for a big class of varieties, however examples for which this duality is understood are very few. In this thesis we investigate the case of Gr(3, 6) with respect to the Plucker embedding.