This is a reference book for academics working in the fields of several complex variables, PDE theory and geometry. The book collects articles on most recent developments in these fields with special emphasis on interactions between them. It includes introductory and expository presentations of the relevant tools, techniques and objects for graduate and PhD students with a corresponding specialization. The volume comprises contributions of leading experts in the field written in a comprehensive and accessible style. Contributors: D. Barlet, S. Berhanu, A. Bove, D.W. Catlin, J.P. D’Angelo, M. Derridj, F. Forstnerič, S. Fu, K. Gansberger, P. Guan, F. Haslinger, B. Helffer, J. Hounie, N. Hungerbühler, F. Lárusson, Ch. Laurent-Thiébaut, L. Lempert, H.-M. Maire, G.A. Mendoza, A. Meziani, N. Mok, M. Mughetti L. Ni, M.-C. Shaw, D.S. Tartakoff, D. Zaitsev