  In these lectures we cover basics of the theory of heights starting with the
heights in the projective space, heights of polynomials, and heights of the
algebraic curves. We define the minimal height of binary forms and moduli
height for algebraic curves and prove that the moduli height of superelliptic
curves $\mathcal H (f) \leq c_0 \tilde H (f)$ where $c_0$ is a constant and
$\tilde H$ the minimal height of the corresponding binary form. For genus $g=2$
and 3 such constant is explicitly determined. Furthermore, complete lists of
curves of genus 2 and genus 3 hyperelliptic curves with height 1 are computed.
