I. Differential Equations with Constant Operator Coefficients -- 1. Power-Exponential Zeros -- 2. Differential Operator Equations in Weighted Sobolev Spaces -- 3. Solutions in a Local Sobolev Space -- 4. Two-Weight L2-Estimates -- II. Differential Equations with Variable Operator Coefficients -- 5. Existence, Uniqueness and โ{128}{156}Pointwiseโ{128}{157} Estimates -- 6. Corollaries of Previous Results Under Special Assumptions on L(t, Dt) -- 7. Two-Weight L2-Estimates for Equations with Variable Coefficients -- 8. Connection of Solutions Corresponding to Different Strips -- 9. Applications to the Case of Perturbations Vanishing at Infinity -- 10. Variants and Extensions of the Previous Theory -- III. Asymptotic Theory of Operator Differential Equations -- 11. Complete Asymptotic Expansions Under Exponential and Power Perturbations of A(Dt) -- 12. Reduction to a First Order System -- 13. General Asymptotic Representation -- 14. Power-Exponential Asymptotics -- 15. The Case of One Simple Eigenvalue on the Line -- 16. Several Simple Eigenvalues on the Line -- 17. The Case of a Single Multiple Eigenvalue -- A. Holomorphic Operator Functions -- A.1 Introduction -- A.2 Prerequisites on Fredholm Operators -- A.3 Basic Notions of the Spectral Theory of Holomorphic Operator Functions -- A.5 The Local Equivalence of Holomorphic Operator Functions -- A.6 The Smith Form of a Holomorphic Matrix Function -- A.7 The Resolvent of a Holomorphic Matrix Function -- A.8 Fredholm Holomorphic Operator Functions -- A.9 The Adjoint Holomorphic Operator Function -- References -- Index of Notation -- Index of Names