In this chapter, we use inversive geometry to construct the model of a hyperbolic plane — a neutral plane that is not Euclidean. Namely, we construct the so-called conformal disc model of the hyperbolic plane. This model was discovered by Beltrami in [4] and often called the Poincaré disk model. The figure above shows the conformal disc model of the hyperbolic plane which is cut into congruent triangles with angles $$\dfrac{\pi}{3}, \dfrac{\pi}{3}$$, and $$\dfrac{\pi}{4}$$.