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. Forstneric, 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. MughettiL. Ni, M.-C. Shaw, D.S. Tartakoff, D. Zaitsev

Oblique Polar Lines of ? X |f|2?|g|2??.- On Involutive Systems of First-order Nonlinear Partial Differential Equations.- Gevrey Hypoellipticity for an Interesting Variant of Kohn's Operator.- Subelliptic Estimates.- Invariant CR Mappings.- On the Subellipticity of Some Hypoelliptic Quasihomogeneous Systems of Complex Vector Fields.- Invariance of the Parametric Oka Property.- Positivity of the -Neumann Laplacian.- Compactness Estimates for the -Neumann Problem in Weighted L 2-spaces.- Remarks on the Homogeneous Complex Monge-Ampère Equation.- A Radó Theorem for Locally Solvable Structures of Co-rank One.- Applications of a Parametric Oka Principle for Liftings.- Stability of the Vanishing of the -cohomoloy Under Small Horizontal Perturbations of the CR Structure in Compact Abstract q-concave CR Manifolds.- Coherent Sheaves and Cohesive Sheaves.- Characteristic Classes of the Boundary of a Complex b-manifold.- Solvability of Planar Complex Vector Fields with Applications to Deformation of Surfaces.- On the Zariski Closure of a Germ of Totally Geodesic Complex Submanifold on a Subvariety of a Complex Hyperbolic Space Form of Finite Volume.- The Large Time Asymptotics of the Entropy.- The Closed Range Property for on Domains with Pseudoconcave Boundary.- New Normal Forms for Levi-nondegenerate Hypersurfaces.