For complex geometry,which really is fundamental in analytic deformation theory,I strongly suggest 2 sources besides the classical source by Griffiths and Harris: Complex Geometry:An Introduction by Daniel Huybrechts,which has rapidly become the standard text on the subject,and the online text draft of a comprehensive work by Demially. The Demailly text is much more comprehensive and more advanced,with an emphasis on algebraic and differential geometry.But you may find it more helpful as it contains a great deal more near the research level. It can be found here: http://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf