Exton has developed 20 triple hypergeometric functions X1 to X20, their Laplace integral representations, reduction and transformation formulas. The present investigation consist of the new results of reducibility, transformations and also integral representations of Euler kind for the Exton's function X1 and X20. In this thesis, we have presented some new techniques to obtain reduction and transformation cases with integral representations for Exton's functions X1 to X20. These results are useful in the study of multiple hypergeometric series.