The intention of this dissertation is to provide general tools and concepts that allow to perform a mathematicallysubstantiated symmetry reduction in (quantum) gauge field theories. Here, the main focus is on the framework of loop quantum gravity (LQG), where we concentrate on the reduction of the quantum configuration space and the construction of normalized Radon measures on the resulting reduced spaces. First, we investigate under which assumptions an action w: G x X -> X is extendible to an action on the spectrum of a C*-algebra of bounded functions on X. Then, we apply this to the framework of LQG where X consists of smooth connections on the underlying principal fibre bundle P. On the one hand, we use this concept to perform a symmetry reduction on quantum level (QR-reduction). On the other hand, we use it to single out measures on symmmetry reduced cosmological configuration spaces by means of their invariance properties. In course of the first issue, we also investigate the question whether quantization and reduction commute or not. Indeed, we show that the quantum-reduced configuration space always (usually even properly) contains the quantized reduced classical space of invariant connections on P (RQ-reduction). In the second part of this work, we construct normalized Radon measures on the symmetry reduced spaces. These define kinematical Hilbert spaces on which the dynamics of the reduced theory can be established in future work. Finally, in the last part, we prove a characterization theorem for invariant connections (reduced classical configuration space) on principal fibre bundles which generalizes the classical results of Wang and Harnad, Shnider and Vinet.