This volume provides a study of the Godbillon-Vey class and other real secondary characteristic classes of transversely holomorphic foliations. One of the main tools in the study is complex secondary characteristic classes. Intended to be self-contained and introductory, this volume contains a brief survey of the theory of secondary characteristic classes of transversely holomorphic foliations. A construction of secondary characteristic classes of families of such foliations is also included. By means of these classes, new proofs of the rigidity of the Godbillon-Vey class in the category of transversely holomorphic foliations are given.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets