Among a number of fundamental issues, the origin of inertial mass remains one of the major open problems in particle physics. Furthermore, topological effects related to non perturbative field configurations are poorly understood in those gauge theories of direct relevance to our physical universe. Motivated by such issues, this Thesis provides a deeper understanding for the appearance of topological effects in abelian gauge field theories, also in relation to the existence of a mass gap for the gauge interactions. These effects are not accounted for when proceeding through gauge fixings as is customary in the literature. The original Topological-Physical factorisation put forth in this work enables to properly identify in topologically massive gauge theories (TMGT) a topological sector which appears under formal limits within the Lagrangian formulation. Our factorisation then allows for a straightforward quantisation of TMGT, accounting for all the topological features inherent to such dynamics. Moreover dual actions are constructed while preserving the gauge symmetry also in the presence of dielectric couplings. All the celebrated mass generation mechanisms preserving the gauge symmetry are then recovered but now find their rightful place through a network of dualities, modulo the presence of topological terms generating topological effects. In particular a dual formulation of the famous Nielsen-Olesen vortices is constructed from TMGT. Within a novel physically equivalent picture, these topological defects are interpreted as dielectric monopoles.