Quantized Partial Differential Equations -- CONTENTS -- Preface -- Quantized PDE's I: Noncommutative Manifolds -- 1.1 - Algebraic topology -- 1.2 - Quantum algebras -- 1.3 - Quantum manifolds -- 1.4 - Quantum supermanifolds -- Quantized PDE's. II: Noncommutative PDE's -- 2.1 - Quantum PDE's -- 2.2 - The quantum Navier-Stokes equation -- 2.3 - Quantum super PDE's -- 2.4 - The quantum super Yang-Mills equations -- Quantized PDE's III: Quantizations of Commutative PDE's -- 3.1 - Integral (co)bordism groups in PDE's -- 3.2 - Algebraic geometry of PDE's -- 3.3 - Spectral measures of PDE's -- 3.4 - Quantizations of PDE's -- 3.5 - Covariant and canonical quantizations of PDE's -- Addendum I: Bordism groups and the (NS)-problem -- 4.0 - Introduction -- 4.1 - Geometry and existence theorems for (NS) -- 4.2 - Navier-Stokes boundary value problems -- 4.3 - The limit case: The Euler equation -- Addendum II: Bordism groups and variational PDE's -- 5.0 - Introduction -- 5.1 - Horizontal and vertical forms on PDE's -- 5.2 - The category of variational PDE's -- 5.3 - Constrained variational sequences -- References -- Index.