On generalized complex geometry

The aim of this thesis is to examine the concept of generalized complex geometry and to investigate some important features related to this concept and to support these features with some examples. For many years, mathematicians and physicists have studied the relationship between mirror symmetry and complex and symplectic geometries. In this thesis, mainly complex and symplectic structures will be studied and the relations between these two structures will be examined. Then, some theories on generalized complex and symplectic geometries will be examined.In addition,the relationship in the contact manifolds with the generalized complex structure is examined. Articles and books on this subject constitute are the main materials for datacollection. The method of the study; firstly, the literature review will be in the form of finding and examining the studies done so far and giving new theories andexamples in the light of the information obtained. That is, the methods used in complex geometry, differantial geometry and theoterical physics during the study are the methods to be used with priority.