Minicourse for master and PhD students. Title: Hilbert scheme of points on a surface and its degeneration. Abstract: Hilbert scheme of zero dimensional subschemes on a (quasi-)projectuve surface gives an interesting construction of higher dimensional smooth (quasi-)projective varieties of even dimension. For example, if the surface is a K3 surface, the Hilbert scheme gives an example of higher dimensional irreducible symplectic projective manifold. In the first part of this mini course, I explain the basic properties of the Hilbert scheme of points only assuming Hartshorne (i.e. a basic knowledge of modern algebraic geometry). In the second part, I put emphasis on the degeneration of Hilbert schemes. The motivation comes from the study of the boundary behavior of the period map of irreducibel symplectic Kähler manifolds. I also explain an explicit construction of the degeneration of Hilbert schemes.