  This is the text of my habilitation thesis defended at the \'Ecole Normale
Sup\'erieure. The topological string presents an arena in which many features
of string theory proper, such as the interplay between worldsheet and target
space descriptions or open-closed duality, can be distilled into computational
techniques which yield results beyond perturbation theory. In this thesis, I
will summarize my research activity in this area. The presentation is organized
around computations of the topological string partition function Z_top based on
various perspectives on the topological string.
