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If you have not heard about cohomology, this book may be suited for you. Fundamental notions in cohomology for examples, functors, representable functors, Yoneda embedding, derived functors, spectral sequences, derived categories are explained in elementary fashion. Applications to sheaf cohomology are given. Also cohomological aspects of D-modules and of the computation of zeta functions of the Weierstrass family are provided.
From the reviews: "This book teems with the author's joy in his subject. It is accordingly an idiosyncratic work, with a variety of human elements poking through the mathematics at nearly every corner. ... Kato's The Heart of Cohomology is a pleasure to read and it'll be a pleasure to come back to it again and again." (Michael Berg, MathDL, December, 2007)