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A basic problem of classical field theory, which has attracted growingattention over the past decade, is to find and classify all nonlineardeformations of linear abelian gauge theories.  The first part of this paper summarizes and significantly elaborates a field-theoretic deformation method developed in earlier work. As a key contributionpresented here, a universal geometrical structure common to a large class ofnonlinear gauge theory examples is uncovered. This structure is derivedgeometrically from the deformed gauge symmetry and is characterized by acovariant derivative operator plus a nonlinear field strength, related throughthe curvature of the covariant derivative. The scope of these resultsencompasses Yang-Mills theory, Freedman-Townsend theory, Einstein gravitytheory, in addition to their many interesting types of novel generalizationsthat have been found in the past several years.  The second part of the paper presents a new geometrical type of Yang-Millsgeneralization in three dimensions motivated from considering torsion in thecontext of nonlinear sigma models with Lie group targets (chiral theories). Thegeneralization is derived by a deformation analysis of linear abelianYang-Mills Chern-Simons gauge theory. Torsion is introduced geometricallythrough a duality with chiral models obtained from the chiral field form ofself-dual 2+2 dimensional Yang-Mills theory under reduction to 2+1 dimensions.Field-theoretic and geometric features of the resulting nonlinear gaugetheories with torsion are discussed.Comment: Published version (misprints corrected and additional references  included) in the special issue of IJGMMP, "Advanced Geometric Techniques in  Gauge Theory

GAUGE THEORY DEFORMATIONS AND NOVEL YANG–MILLS CHERN–SIMONS FIELD THEORIES WITH TORSION