Table of contents : Front Matter....Pages i-viii Introduction....Pages 1-5 Local Theory of Complex Spaces....Pages 7-96 Differential Calculus, Holomorphic Maps and Linear Structures on Complex Spaces....Pages 97-144 Cohomology....Pages 145-182 Seminormal Complex Spaces....Pages 183-220 Pseudoconvexity, the Levi Problem and Vanishing Theorems....Pages 221-257 Theory of q -Convexity and q -Concavity....Pages 259-284 Modifications....Pages 285-317 Cycle Spaces....Pages 319-349 Extension of Analytic Objects....Pages 351-360 Back Matter....Pages 361-372