We do not have time to do very much in the way of model solution methods.
The basic reference on solution methods is Judd's textbook.
On nonlinear methods, see also Christiano and Fisher (this paper is published in the Journal of Economic Dynamics and Control).
For a recent paper on assessing the accuracy of non-linear solution methods, see Santos.
In our discussion of policy in the absence of commitment, we considered the Klein-Krusell-Rios Rull perturbation method for computing differentiable Markov equilibria. The Sims and Schmit-Grohe, Uribe papers were also mentioned.
In the course, we will focus primarily on the linearization method described in Christiano, 'Solving Dynamic Equilibrium Models by a Method of Undetermined Coefficients' (manuscript, computer code).