*Two-dimensional gauge theory * In the first part of the talk a pedagogical review of the analytic methods in Lattice Field Theory will be given. Topics to be covered are: euclidean partition function, character expansion, gauge fixing, transfer matrix, continuum limit, Feynman kernel, etc. These methods will then be applied to calculate analytically, partition function, and various observables in the two-dimensional pure gauge theory. Effect of boundary conditions, and emergence of the topological charge, will be also illustrated by explicit calculations. Exact Coulomb gauge will be constructed on the lattice and the effective, one degree of freedom, Manton’s hamiltonian rederived from the lattice approach. Generalization for the system with external charges will be also given. In particular, Manton’s parameter will be explicitly calculated in this case. Finally, if time permits, some less orthodox issues, like description of non-integer, external charges will be introduced.

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