Calabi-Yau spaces are used to construct possibly realistic (super)string models and are thus being studied vigorously in the recent physics literature. In the main part of this book, the authors collect and review the relevant results on (1) several major construction techniques, (2) computation of physically relevant quantities such as massless field spectra and the Yukawa interactions, (3) stringy corrections, (4) moduli space and its geometry. In addition, a preliminary discussion of the conjectured universal moduli space and related open problems are included. The authors also include several detailed models to exemplify the techniques and the general discussion. This is probably to be the first systematic exposition in book form of the material on Calabi-Yau spaces, otherwise scattered through conference proceedings and journals.