In the present project, we will review the classical theory of the Sine-Gordon model, a nonlinear model of dispersive wave propagation with numerous applications, which can be obtained as the continuous limit of a discrete mechanical system. The equation of the model is derived from a system of pendulums coupled through a harmonic potential, and some of its solutions—such as solitons—are studied. Subsequently, we examine the equivalence between the (1+1)-dimensional Sine-Gordon model and the two-dimensional Coulomb gas in the case of thermal equilibrium and overall electric neutrality, with the goal of deriving the thermodynamics of this system from the Sine-Gordon formalism.