Hyperbolic geometry is a non-Euclidean geometry that differs from the familiar Euclidean geometry. In hyperbolic geometry, the parallel postulate of Euclid is replaced, allowing for multiple lines to pass through a point not on a given line without intersecting it. This creates a space where the angles of a triangle sum to less than 180 degrees, leading to unique properties and shapes. In hyperbolic geometry, the Poincaré disk model and the hyperboloid model are common representations. These models help visualize hyperbolic space, where distances and angles behave differently than in flat, Euclidean space. This geometry has applications in various fields, including theoretical physics and art.