The 18 invited lectures explore a new branch of mathematics and mathematical physics arising from the intersection of the geometry of nonlinear differential equations, quantum field theory, and cohomological algebra. They include recent results in cohomological aspects of quantum field theory and the geometry of partial differential equations; a new look at interrelations among the related fields; and applications to Batalin-Vilkovisky formalism, BRST formalism, anomalies, and quantum dynamics. Accessible to professional and advanced graduate mathematicians. No index. Annotation copyrighted by Book News, Inc., Portland, OR