This book collects various perspectives contributed by both mathematicians and physicists on
the B-model and its role in mirror symmetry. Mirror symmetry is an active topic of research in
both the mathematics and physics communities but among mathematicians the A-model half of the
story remains much better-understood than the B-model. This book aims to address that
imbalance. It begins with an overview of several methods by which mirrors have been constructed
and from there gives a thorough account of the BCOV B-model theory from a physical perspective
this includes the appearance of such phenomena as the holomorphic anomaly equation and
connections to number theory via modularity. Following a mathematical exposition of the subject
of quantization the remainder of the book is devoted to the B-model from a mathematician's
point-of-view including such topics as polyvector fields and primitive forms Givental's
ancestor potential and integrable systems.
