The study of space originates from Euclidean geometry, while trigonometry combines space with numbers, including the famous Pythagorean theorem, trigonometric function and so on. Nowadays, the study of space extends to high-dimensional geometry, non-Euclidean geometry and topology. Numbers and spaces play an important role in analytic geometry, differential geometry and algebraic geometry. In differential geometry, there are concepts such as fiber bundle and calculation on manifold. In algebraic geometry, there are descriptions of geometric objects such as solution sets of polynomial equations, which combine the concepts of number and space. There is also the study of topological groups, which combines structure and space. Lie groups are used to study space, structure and change.