Abstract: A Gaussian analytic function is a linear combination of analytic functions with the coefficients being drawn independently from the standard complex normal distribution. We shall explain three classical results about distribution of zeroes of Gaussian analytic functions in the complex plane:

(1) the Edelman-Kostlan formula for the "typical" (or average) distribution of zeroes;

(2) Calabi's rigidity: the average distribution of zeroes ``determines'' the Gaussian analytic function;

(3) Offord's estimate: the probability that the distribution of zeroes of a Gaussian analytic function deviates from the typical one by some fixed amount s is about exp(-const s).