I have found an article by Huebschmann, Rudolph and Schmidt about "A Gauge Model for Quantum Mechanics on a Stratified Space" and I am very interested in this subject, but I don't have any background in gauge-field theory or something like that.

So my question is, if there are any good introductory books or overview articles which cover **Hamiltonian (quantum) gauge field theory on the lattice in a geometrical mathematical language** like the article mentioned above? Especially I am interested in references which deal with more regular cases rather than the singular cases discussed in the article above. Finally it is important that it covers this topic in a way that one can gain a bit deeper physical understanding (without giving up a clear, rigorous and geometrical mathematical language).

**Added**
Thanks for your answers. Gauge field theory seems to be a very wide field, so I should perhaps mention why I want to learn some basics about gauge field theory beside of very strong intrinsic interest.

I am studying phase-space reduction in the context of deformation quantization of systems with finite degrees of freedom. Now I want to know if it is possible to reinterpret this situation (at least as a toy model) in some way in terms of gauge field theories. So my aim is to learn at least as much of gauge field theory that I can understand if and why such an reinterpretation is possible or how far one can go.

The idea to look for **lattice** gauge theories was the following quote from the paper by Huebschmann et. al.

Gauge theory in the Hamiltonian approach, phrased on a finite spatial lattice, leads to tractable finite-dimensional models for which one can analyze the role of singularities explicitly. Under such circumstances, after a choice of tree gauge has been made, the unreduced classical phase space amounts to the total space $\mathrm{T}^* (K \times \dots \times K)$ of the cotangent bundle on a product of finitely many copies of the manifold underlying the structure group $K$. Gauge transformations are then given by the lift of the action of $K$ on $K \times \dots \times K$ by diagonal conjugation. This leads to a finite-dimensional Hamiltonian system with symmetries.

Why a asked for a "geometric language" is clear because the strength of deformation quantization is in fact in the area of the quantization of systems with a more complex phase-space geometry.

Having this additional information it is perhaps easier for you to give me some hints where to start in literature.