You may begin with the following four books. After having gone through them, you may come back and I shall be able to provide you with more relevant references:

[1] P Fazekas, Lecture Notes on Electron Correlation and Magnetism (World Scientific, Singapore, 2003).

[2] F Gebhard, The Mott Metal-Insulator Transition: Models and Methods (Springer, Berlin, 1997).

[3] A Montorsi, editor, The Hubbard Model: A Reprint Volume (World Scientific, Singapore, 1992).

[4] M Rasetti, editor, The Hubbard Model: Recent Results (World Scientific, Singapore, 1991).

I would try to have a go at reading the references quoted above, as provided by Behnam.

But, in brief, a basic overview of the Hubbard model may be described as a model that attempts to understand the potential energy of a charge carrier (such as an electron or hole, etc) hopping/moving between available sites within the crystal lattice and then from that try to explain the electrical transport properties of a material, i.e. why something might behave as a metal or an insulator or how a material transitions from a metal-insulator, etc.

When you mention the Anderson model, I presume you mean the Resonance Valence Bond (RVB) theory that P. W. Anderson proposed relating to high-Tc superconductors? If so, you can think of it simply as a model that tries to explain high-Tc superconductors by thinking of the Cooper pairs as existing as bound valence electrons that become free flowing above some critical pressure. For instance, in the cuprates, such as YBCO, when the oxygen content is low it exists as a antiferromagnetic Mott insulator where the electrons are ordered antiparallel and the Hubbard potential is very large leading to an insulating state, where the electrons are bound to their sites in the lattice very firmly, but as you dope it with more oxygen (increasing the chemical pressure by adding more oxygen into the lattice) it eventually reaches a critical doping and becomes a superconductor! Anderson proposed that the superconducting state is already 'pre-formed' in the antiferromagnetic Mott insulating state in the form of bound valence electrons that become free when YBCO is doped. I would recommend reading Anderson's original paper..or in fact any papers written by Anderson. They can be difficult to read when you're new to the subject, but very insightful.

Hope this helps in some way.

Dear Alexander,

No, by Anderson Model  one generally refers the Anderson impurity model. I had indented to present references to some literature specific to this model later on, partly not to overwhelm the page with excessive references and partly because of the fact that the literature dealing with this model is truly vast, with some remarkable contributions that neglecting any of them would amount to doing injustice to their authors. Below I present a small selection of the relevant references.

A detailed discussion of the Anderson impurity model is presented in

[1] AC Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, 1993).

The following is a first of a series of papers on a perturbative treatment of this model:

[2] K Yosida, and K Yamada, Suppl. Prog. Theor. Phys. 46, 244 (1970).

The following is again one of a series of papers on a novel perturbative treatment of the Anderson Hamiltonian:

[3] K Keiter, and C Kimball, Int. J. Mag. 1, 233 (1971).

The celebrated non-crossing approximation (NCA) amounts to taking account of the non-crossing diagrams of the kind introduced in the above paper. The NCA is discussed in

[4] P Fulde, Electron Correlation in Molecules and Solids, 3rd edition (Springer, Berlin, 1995).

And the following is a review of the 1/N expansion treatment of the Anderson model:

[5] NE Bickers, Rev. Mod. Phys. 59, 845 (1987).  □