2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56164This thesis presents a thorough analysis of the links between the N=4 supersymmetric gauge theory in four dimensions and its three topological twisted counterparts. Special emphasis is put in deriving explicit results in terms of the vacuum structure and low-energy effective description of four-dimensional supersymmetric gauge theories. A key ingredient is the realization of Montonten-Olive duality in the twisted theories, which is discussed in detail from different viewpoints.Doctoral Thesis, LaTex2e, 157 pages, uses amsmath and epsfig packages, 1 PostScript figure. Revised version: typos corrected, discussion on Vafa-Witten partition function improvedHigh Energy Physics - Theorytext