D modules perverse sheaves and representation theory This work examines in detail the foundations of D module theory and its intersection with cohomology groups and representation theory. This systematic and carefully written exposition begins with preliminary concepts before focusing on some basic but important theories that have emerged in the last few decades. Significant topics that have emerged as studies in their own right include a treatment of the theory of holonomic D modules perverse sheaves the Riemann Hilbert correspondence Hodge modules and Kazhdan Lusztig polynomials. To further aid the reader appendices are provided as reviews for the theory of derived categories and algebraic varieties. D modules Perverse Sheaves and Representation Theory is a unique and essential textbook at the graduate level for classroom use or self study. Graduate students and researchers in algebra and representation theory willbenefit greatlyfrom this work. TOC:Introduction Part I. D modules Preliminary notions Coherent D modules Holonomic D modules and its solutions Theory of meromorphic connections Regular holonomic D modules Perverse sheaves and intersection cohomologies Hodge module Part II. Algebraic Groups Algebraic groups and Lie algebras Conjugacy classes of semisimple Lie algebras Representations of Lie algebras and D modules Character formula of highest weight modules Hecke algebras and Hodge modules A. Algebraic Varieties B. Derived categories and derived functors References Index