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本书作者Jean-Pierre Demailly 教授是法国格勒诺布尔最大学数学系教授,著名数学家,1994年获选为法国科学院院士. 本书讲述代数几何中的分析方法，该方法广泛地应用于线性系列，代数向量丛的消失定理等。 This volume is an expansion of lectures given by the author at the Park City Mathematics Institute in 2008 as well as in other places. The main purpose of the book is to describe analytic techniques which are useful to study questions such as linear series, multiplier ideals and vanishing theorems for algebraic vector bundles. The exposition tries to be as condensed as possible, assuming that the reader is already somewhat acquainted with the basic concepts pertaining to sheaf theory, homological algebra and complex differential geometry. In the final chapters, some very recent questions and open problems are addressed, for example results related to the finiteness of the canonical ring and the abundance conjecture, as well as results describing the geometric structure of K\"ahler varieties and their positive cones.
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