Gauge Field theories (cf. [Ry], [Po], [Q], [Ru], [Fr], [ChNe], [Pol], and [AH]) have had a great impact in modern theoretical physics, as they keep internal symmetries and can account for important physical phenomena such as: spontaneous symmetry breaking (see e.g., [En1], [En2], and [Br]), the quantum Hall effect (see e.g., [GP], [Gi], [McD], [Fro], and [Sto]), charge fractionalization, superconductivity, and supergravity (see e.g., [Wi], [Le], [GL], [Park], [Sch], [Ti], and [KeS]). In these notes, we focus on specific examples of gauge field theories which admit a selfdual structure when the physical parameters satisfy a “critical” coupling condition that typically identifies a transition between different regimes. The selfdual regime is characterized by the presence of “special” soliton-type solutions corresponding to minimizers of the energy within certain constraints of “topological” nature. Such solutions, known as selfdual solutions, satisfy a set of first-order (selfdual) equations that furnish a “factorization” for the second-order gauge field equations. Furthermore, each class of “topologically equivalent” selfdual solutions form the space of moduli, whose characterization is one of the main objectives in gauge theory.