Various extended objects in string theory, collectively named branes, have played a crucial role in the exciting recent development of the theory. A delicate interplay between the two dual description of the branes, namely the world-volume and spacetime theories, has revealed a rich structure possessed by the branes and the string theory they live in. The main goal of this thesis is to study examples of such interplay. In the first part, we study some special cases of branes ending on other branes. The results give a hint on a precise connection between the two dual descriptions, which has been recently made concrete by the conjectured correspondence between some superconformal field theory (SCFT) and string theory in the anti-de-Sitter (AdS) background. The second part of the thesis is devoted to computing correlation functions of D = 4, N = 4 supersymmetric Yang-Mills (SYM) theory using this correspondence.
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