Natural gas is an important source of energy that is regarded as essential for achieving the politically set climate goals. In particular, gas-fired power plants are valued as flexible buffers to compensate for fluctuations in renewable electricity generation. Moreover, gas network operators face new challenges due to the liberalization of the European gas market. Under the newly introduced entry-exit market regime, gas network operators have to ensure that all possible market outcomes can be transported over the network. Hence, the operators of gas networks require new aids for decision-making under uncertain conditions such as load fluctuations or inaccuracies in physical parameters. To this end, this thesis investigates a general class of two-stage robust optimization problems using the example of gas network operations under uncertainty. Three general solution methods are developed for this problem class. The first two approaches use ideas from polynomial optimization to decide robust feasibility or infeasibility. Both procedures consider polynomial formulations that are approximated by semidefinite programs via the Lasserre relaxation hierarchy. The third approach is based on a transformation of the two-stage robust problem into a number of single-stage optimization problems. The resulting subproblems are approximated by mixed-integer linear programs. By combining this method with additional preprocessing and aggregation steps, it is demonstrated that real-world problems can be solved efficiently within a short time.weiterlesen