(untitled) (The São Paulo Journal of Mathematical Sciences, 2009)
The present paper is an exposition on heights and their importance in the modern study of algebraic dynamics. We will explain the idea of canonical height and its surprising relation to algebraic dynamics, invariant measures, arithmetic intersection theory, equidistribution and p-adic analytic geometry. AMS Classification 2000:Primary: 14G40; Secondary: 11G50, 28C10,14C17. Keywords: height function, algebraic dynamics, analytic spaces.