This book covers an exciting interplay between arithmetic and dynamical systems. The fulcrum is a natural measure of height of a polynomial, known as Mahler's measure. In dynamical systems, this same measure arises as the entropy - a measure of orbit complexity - of a map associated to the polynomial. Over 100 exercises are included, each with outline solutions, together with a list of open problems. The book provides an ideal introduction to the field for advanced undergraduate and postgraduate students.