In this paper we deal with the approximation and interpolation of a function. Approximation involves determining the function that will best describe a given data set or other function with the smallest deviation, and interpolation is the requirement that the values of some two functions match at some finite set of points. The general problem of approximation, the criterion of approximation and the interpolation of polynomials are considered further in this paper. Interpolation by polynomials is made through Lagrange’s and Newton’s form of interpolation polynomial with examples and algorithms written in the programming language C. The content is expanded with Hermite interpolation, where in each node, we also interpolate the derivation value. For some functions, increasing the degree of the polynomial interpolant, can lead to an increase of errors and instead of interpolation by polynomials with high degree, we can use interpolation by piecewise polynomials. In the end of the paper we deal with the method of least squares. With this method we can approximate a given function by another function globally in contrast to the Lagrange polynomial, which well approximates the function locally at selected points.