Topological weights and combinatorical unitarity in first and second quantization

We give a unified and coherent account on particle and string theories with a particular emphasis on the comparison of first and second quantization. The formalism described is applicable to other (higher dimensional) propagating objects. The weights of topologically different graphs determine the possible interactions. Restrictions on them, imposed by combinatorical aspects of unitarity are discussed. These restrictions are particularly strong for string theories. Reparametrization and modular invariance are also considered in this light. (orig.)