From the reviews: "... focused mainly on complex differential geometry
and holomorphic bundle theory. This is a powerful book, written by a
very distinguished contributor to the field" (Contemporary Physics )"the
book provides a large amount of background for current research across a
spectrum of field. ... requires effort to read but it is worthwhile and
rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly
technical and the pace of the exposition is quite fast. Manin is an
outstanding mathematician, and writer as well, perfectly at ease in the
most abstract and complex situation. With such a guide the reader will
be generously rewarded!" (Physicalia) This new edition includes an
Appendix on developments of the last 10 years, by S. Merkulov.