Authors: Joseph KRASIL'SHCHIK, Alexander VERBOVETSKY

Lectures given in August 1998 at an advanced 5-day course in Levoca, Slovakia.

These lecture notes are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations: the Vinogradov C- spectral sequence and the C-cohomology, including the formulation in terms of the horizontal (characteristic) cohomology. Applications to computing invariants of differential equations are discussed. The lectures contain necessary introductory material on the geometric theory of differential equations and homological algebra.

146 pages, LaTeX-2e (AmSLaTeX 1.2).

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