  The aim of this paper is to present a self contained introduction to the
Hubbard model and some of its applications.The paper consists of two parts: the
first will introduce the basic notions of the Hubbard model starting from the
motivation for its development to the formulation of the Hamiltonian,and some
methods of calculation within the model. The second part will discuss some
applications of the model to 1D and 2D systems,based on a combination of the
author's results with those from the literature.
