Analytic Theory of Polynomials: Critical Points, Zeros and Extremal PropertiesThis text presents easy to understand proofs of some of the most difficult results about polynomials. It encompasses a self contained account of the properties of polynomials as analytic functions of a special kind. The zeros of compositions of polynomials are also investigated along with their growth, and some of these considerations lead to the study of analogous questions for trigonometric polynomials and certain transcendental entire functions.