Description: Preface to the English Translation. Preface to the Russian edition. Introduction. List of main notations. 1. Resolution of differential operators. 2. Parametrices and fundamental solutions of differential complexes.3. Sokhotskii-Plemelj formulas for elliptic complexes. 4. Boundary problems for differential complexes. 5. Duality theory for cohomologies of differential complexes. 6. The Atiyah-Bott-Lefschetz theorem on fixed points for elliptic complexes. Bibliography. Name index. Subject index. Index of notation.