The book addresses a key question in topological field theory and logarithmic conformal field
theory: In the case where the underlying modular category is not semisimple topological field
theory appears to suggest that mapping class groups do not only act on the spaces of chiral
conformal blocks which arise from the homomorphism functors in the category but also act on
the spaces that arise from the corresponding derived functors. It is natural to ask whether
this is indeed the case. The book carefully approaches this question by first providing a
detailed introduction to surfaces and their mapping class groups. Thereafter it explains how
representations of these groups are constructed in topological field theory using an approach
via nets and ribbon graphs. These tools are then used to show that the mapping class groups
indeed act on the so-called derived block spaces. Toward the end the book explains the
relation to Hochschild cohomology of Hopf algebras and the modular group.
