Some of the key cohomological features of the two $(1+1)$-dimensional (2D)free Abelian- and self-interacting non-Abelian gauge theories (having nointeraction with matter fields) are briefly discussed first in the language ofsymmetry properties of the Lagrangian densities and the same issues aresubsequently addressed in the framework of superfield formulation on the four($2 + 2)$-dimensional supermanifold. Special emphasis is laid on the on-shell-and off-shell nilpotent (co-)BRST symmetries that emerge after the applicationof (dual) horizontality conditions on the supermanifold. The (anti-)chiralsuperfields play a very decisive role in the derivation of the on-shellnilpotent symmetries. The study of the present superfield formulation leads tothe derivation of some new symmetries for the Lagrangian density and thesymmetric energy-momentum tensor. The topological nature of the above theoriesis captured in the framework of superfield formulation and the geometricalinterpretations are provided for some of the topologically interestingquantities.
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