These notes cover some of the basic properties of Gaussian analytic functions with emphasis on their zeros. Also included are the essentials of determinantal point processes. One of the goals is to compare and contrast the similarities and difference between the zero process of the Gaussian Entire Function and the infinite Ginibre ensemble (limit of eigenvalue process of non-Hermitian complex Gaussian matrices). These are point processes whose distribution is invariant under isometries of the plane, whose features are quite different from the ones of the homogeneous Poisson point process.