In this chapter, Lagranges and Hermits interpolation by polynomials, by trigonometric polynomials, by Chebyshevs polynomials and by generalized polynomials spanned on Chebyshevs systems of coordinates are presented. Lagranges and Newtons formulas to find the interpolating polynomials are derived and clarified. Mathematica modules are designed to determine interpolating polynomials. Fundamental theorems on interpolation with the errors bounds are stated and proved. The application of the theorems has been elucidated by examples. The Chapter ends with a set of questions.
Keywords: Lagrange polynomials, Newton polynomials, Chebyshev polynomials.