One of the main ingredients of high-order numerical solutions of PDEs is finding an approximation for the spatial derivative of a function given its point-wise values, to which the linear polynomial interpolation is a simple, efficient approach. We begin this chapter with the linear polynomial interpolation in one-space dimension [1]. We then address the errorInterpolationerror analysis of the interpolation approximation. For an equispaced grid and an increasingly high number of interpolation points (or increasingly high polynomial degrees), we highlight the non-uniform error distribution over the approximation domain.