Modelling Hyperbolic Geometry

In Euclidean geometry we have the following: Given a line L and a point P not on it, there is exactly one line through P that is parallel to L. It was discovered that assuming this is false produces the equally valid Hyperbolic Geometry, where there are in fact infinitely many lines through P that are parallel to L. This presentation is an introduction to Hyperbolic Geometry, and on modelling it in the Euclidean plane.