Exact results are exceedingly rare in physics. An important exactly soluble model, originally designed to model 2D ice, is the six-vertex model. For a system with macroscopically large number of degrees of freedom, getting 'exact solution' implies that we will exactly diagonalize the Hamiltonian. This will be done using a powerful technique known as the Bethe Ansatz. We then take suitable limits to extract relevant thermodynamic properties of the system. A very unique thermodynamic property of ice is that it has nonzero entropy at absolute zero temperature. The principal result we obtain in this class will be this residual entropy of 2D ice.