Algebraic and combinatorial methods in the theory of set addition

This report contains a good part of the results of my reserach in additive combinatorics I have been conducting during the last decade, the central theme being the structural theory of set addition. The four main chapters contain results obtained by four different methods reflected in their respective titles, most prominently by the so-called polynomial method. The results in the first three of those chapters nicely fit into a general framework that we explain in the introduction. The last chapter appears to be out of this context at a first glance. Most of the results therein, however, can be traced back to the Erdös--Heilbronn problem, which is in the center of these investigations.