This paper introduces generalized Calabi-Yau manifolds, which generalize both Calabi-Yau and symplectic manifolds. These structures are defined on even-dimensional manifolds and can be transformed by diffeomorphisms and closed 2-forms. In six dimensions, they are characterized as critical points of a natural variational problem on closed forms, and their local moduli space is given by an open set in either the odd or even cohomology. The paper defines generalized complex and Calabi-Yau manifolds using the Courant bracket and the B-field. It shows that generalized Calabi-Yau structures can be transformed by closed 2-forms and that they include both Calabi-Yau and symplectic manifolds as special cases. The paper also discusses the moduli space of these structures, showing that it is an open set in the corresponding cohomology group under certain conditions. The paper concludes with a discussion of the pseudo-Kähler structure on the moduli space and the role of the Courant bracket in defining the generalized Calabi-Yau structures.This paper introduces generalized Calabi-Yau manifolds, which generalize both Calabi-Yau and symplectic manifolds. These structures are defined on even-dimensional manifolds and can be transformed by diffeomorphisms and closed 2-forms. In six dimensions, they are characterized as critical points of a natural variational problem on closed forms, and their local moduli space is given by an open set in either the odd or even cohomology. The paper defines generalized complex and Calabi-Yau manifolds using the Courant bracket and the B-field. It shows that generalized Calabi-Yau structures can be transformed by closed 2-forms and that they include both Calabi-Yau and symplectic manifolds as special cases. The paper also discusses the moduli space of these structures, showing that it is an open set in the corresponding cohomology group under certain conditions. The paper concludes with a discussion of the pseudo-Kähler structure on the moduli space and the role of the Courant bracket in defining the generalized Calabi-Yau structures.