Holomorphic Functions -- Complex Manifolds -- Differential Forms, Vector Bundles, Sheaves -- Infinitesimal Deformation -- Theorem of Existence -- Theorem of Completeness -- Theorem of Stability.From the reviews: "The author, who with Spencer created the theory of deformations of a complex manifold, has written a book which will be of service to all who are interested in this by now vast subject. Although intended for a reader with a certain mathematical maturity, the author begins at the beginning, [...]. This is a book of many virtues: mathematical, historical, and pedagogical. Parts of it could be used for a graduate complex manifolds course." J.A. Carlson in Mathematical Reviews, 1987 "There are many mathematicians, or even physicists, who would find this book useful and accessible, but its distinctive attribute is the insight it gives into a brilliant mathematician's work. [...] It is intriguing to sense between the lines Spencer's optimism, Kodaira's scepticism or the shadow of Grauert with his very different methods, as it is to hear of the surprises and ironies which appeared on the way. Most of all it is a piece of work which shows mathematics as lying somewhere between discovery and invention, a fact which all mathematicians know, but most inexplicably conceal in their work." N.J. Hitchin in the Bulletin of the London Mathematical Society, 1987.