Intended for researchers, this book reviews the geometry of D- schemes, then explains the basic local and global aspects of chiral algebra theory. The authors consider basic chiral algebra structures and their interrelations, describe elementary methods of constructing chiral algebras, formalize chiral homology as a quantum version of the space of global horizontal section of an affine Dx-scheme, define a canonical Batalin-Vilkovisky algebra structure on the chiral chain complex, and develop two flat projective connections on the chiral homology sheaves.