This webpage serves as an introduction to the psychedelic and profound world of non-Euclidean geometry. We will start from the rebellious and mind-wracking history of its 2000-year development, a struggle that tormented generations. The ideas of elliptical and hyperbolic geometry emerged from these fires of mind and revolutionized the way we thought about space. Elliptical and hyperbolic geometry served as the gateways into infinite possibilities for non-Euclidean geometry which are classified by their curvatures. The study of curvature has recently experienced a discrete reformulation spurred by the animation industry, which helps to makes the non-Euclidean concepts more intuitive. Lastly, we cannot forget the incredible importance of these tools in modeling the geometry of space and time around Earth, the nature of gravity, and shape of our universe.