This thesis is concerned with D-branes in topological string theory, focusing
on the description of B-type D-branes in topological Landau-Ginzburg models.
Such D-branes are characterized by matrix factorizations of the Landau-Ginzburg
superpotential. After reviewing some aspects of topological string theory we
give a detailed discussion of matrix factorizations. We discuss methods to
calculate the effective superpotential in minimal models, putting emphasis on
an algorithm to calculate the effective superpotential via deformations of
matrix factorizations. We furthermore perform a non-trivial check of
homological mirror symmetry for the torus.Comment: PhD thesis, 147+9 pages, 10 figure