In this thesis, we give an expanded account of shift operators on Banach spaces. A bounded linear operator T on Banach space E is called a forward shift if 1. is an isometry; 2. The range of T has codimension 1; 3. . Also a bounded linear operator T on Banach space E is a backward shift if 1. 2. The linear transformation is isometry; where is induced by T and defined as for any ; 3. is dense in . The aim of this thesis, the study unilateral shift operators on Banach spaces and in particular some, spaces of continuous functions. The general question which arises then the concept of shift operators, is which of Banach spaces admit the shift operators? In this regard, we examine the general characteristics of the shift operators on Banach spaces. We define the concept of forward and backward shift on Banach spaces, and then we study the properties of this shifts. Also we check presence or absence of shifts on some product spaces. At the end, focus of the relationship between of the forward and backward shift operators on a Banach space and its dual. We consider a compact Hausdorff space X and evaluate the shift operators on the function space C(X).