Nonlinear geometry is a branch of mathematics that studies shapes and spaces that do not follow traditional linear rules. Unlike linear geometry, which deals with straight lines and flat surfaces, nonlinear geometry explores curves, surfaces, and higher-dimensional spaces that can bend and twist in complex ways. This field is essential for understanding phenomena in various scientific disciplines, including physics and computer graphics. One of the key concepts in nonlinear geometry is the idea of curvature, which measures how much a geometric object deviates from being flat. Nonlinear geometric principles are applied in areas such as general relativity, where the fabric of spacetime is curved by mass, and in machine learning, where complex data relationships are modeled using nonlinear structures.