We offer computationally convenient and effective schemes of interpolation and extrapolation. These methods are ideal for any system that needs to work with functions which are stored in tabular form. We include the methods of Newton polynomials, Lagrange's formula, Burlisch-Stoer algorithm, Cubic splines (natural and free) and Bicubic interpolation. We also consider algorithms for finding the coefficients of an interpolation function and interpolation in higher dimensions.