Generalized complex geometry encompasses both complex and symplectic geometry as special cases. This geometry is characterized by enhanced symmetry groups, elliptic deformation theory, connections to Poisson geometry, and local structure theory. The book explores these aspects in detail, including the definition and study of generalized complex branes, which interpolate between flat bundles on Lagrangian submanifolds and holomorphic bundles on complex submanifolds. The first part of the book focuses on the linear geometry of \(T \oplus T^*\), including symmetries, maximal isotropic subspaces, spinors, the Mukai pairing, pure spinors, and the spin bundle. The second part introduces the Courant bracket, its symmetries, relation to \(S^1\)-gerbes, and Dirac structures. The third part delves into generalized complex structures, their integrability, Hamiltonian symmetries, and the Poisson structure. The fourth part proves a local structure theorem for generalized complex manifolds, similar to the Darboux theorem in symplectic geometry. The fifth part develops the deformation theory of generalized complex manifolds, governed by a differential Gerstenhaber algebra. The sixth part introduces generalized complex branes, which are vector bundles supported on submanifolds with specific properties. The book is based on the author's doctoral thesis and provides a comprehensive exploration of generalized complex geometry, supported by numerous examples and detailed proofs.Generalized complex geometry encompasses both complex and symplectic geometry as special cases. This geometry is characterized by enhanced symmetry groups, elliptic deformation theory, connections to Poisson geometry, and local structure theory. The book explores these aspects in detail, including the definition and study of generalized complex branes, which interpolate between flat bundles on Lagrangian submanifolds and holomorphic bundles on complex submanifolds. The first part of the book focuses on the linear geometry of \(T \oplus T^*\), including symmetries, maximal isotropic subspaces, spinors, the Mukai pairing, pure spinors, and the spin bundle. The second part introduces the Courant bracket, its symmetries, relation to \(S^1\)-gerbes, and Dirac structures. The third part delves into generalized complex structures, their integrability, Hamiltonian symmetries, and the Poisson structure. The fourth part proves a local structure theorem for generalized complex manifolds, similar to the Darboux theorem in symplectic geometry. The fifth part develops the deformation theory of generalized complex manifolds, governed by a differential Gerstenhaber algebra. The sixth part introduces generalized complex branes, which are vector bundles supported on submanifolds with specific properties. The book is based on the author's doctoral thesis and provides a comprehensive exploration of generalized complex geometry, supported by numerous examples and detailed proofs.