In this publication a tropical intersection theory is established with analogue notions and tools as its algebro-geometric counterpart. The developed theory, interesting as a subfield of convex geometry on its own, shows many relations to the intersection theory of toric varieties and other fields. In the second chapter, tropical intersection theory is used to define and study tropical gravitational descendants (i.e. Gromov-Witten invariants with incidence and "Psi-class" factors). It turns out that many concepts of the classical Gromov-Witten theory such as the WDVV equations can be carried over to the tropical world.

Johannes Rau studied algebraic geometry at TU Kaiserslautern. Hereceived his diploma degree in 2005 and his Ph.D. degree in 2009under supervision of Andreas Gathmann. In fall 2009, Rau attendedthe program on tropical geometry at MSRI, Berkeley.

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