Lobachevskian Geometry, also known as hyperbolic geometry, is a non-Euclidean geometry developed by the mathematician Nikolai Lobachevsky in the 19th century. In this geometry, the parallel postulate of Euclidean Geometry is replaced, allowing for multiple lines through a point that do not intersect a given line. This leads to unique properties, such as the sum of angles in a triangle being less than 180 degrees. In Lobachevskian Geometry, shapes and figures behave differently than in traditional geometry. For example, the concept of distance and area is altered, resulting in a space that can be visualized as a saddle shape. This geometry has applications in various fields, including theoretical physics and art, influencing how we understand space and dimensions.