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.