A Russian mathematician named Nikolai Ivanovich Lobachevsky is the man credited with inventing hyperbolic geometry. Nikolai lived from 1792 to 1856.
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Hyperbolic geometry is used very often in space, such as space travel and gravitational pulls and rotations of planets. This geometry is used most often in space because of Einstein's general Theory of Relativity assumes that space is not a Euclidean space, but a hyperbolic one.
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One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.