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The purpose of this article is to present a pedagogical review of T-dualityinin string theory. The evolution of the closed string is envisaged on theworldsheet in the presence of its massless excitations. The duality symmetry isstudied when some of the spacial coordinates are compactified on d-dimensionaltorus, $T^d$. The known results are reviewed to elucidate that equations ofmotion for the compact coordinates are $O(d,d)$ covariant, $d$ being the numberof compact directions. Next, the vertex operators of excited massive levels areconsidered in a simple compactification scheme. It is shown that the vertexoperators for each massive level can be cast in a T-duality invariant form insuch a case. Subsequently, the duality properties of superstring isinvestigated in the NSR formulation for the massless backgrounds such asgraviton and antisymmetric tensor. The worldsheet superfield formulation isfound to be very suitable for our purpose. The Hassan-Sen compactification isadopted and it is shown that the worldsheet equations of motion for compactsuperfields to be very suitable for our purpose. The Hassan-Sencompactification is adopted and it is shown that the worldsheet equations ofmotion for compact superfields are $O(d,d)$ covariant when the backgrounds areindependent of superfields along compact directions. The vertex operators forexcited levels are presented in the NS-NS sector and it is shown that they canbe cast in T-duality invariant form for the case of Hassan-Sen compactificationscheme. An illustrative example is presented to realize our proposal.

The Worldsheet Perspective of T-duality Symmetry in String Theory