Mathematical analysis (English: Mathematical Analysis) is the oldest and most basic branch of analysis, which is different from the advanced mathematics content of other non-mathematics majors. Generally speaking, it refers to a relatively complete mathematical discipline with the general theory of calculus, infinite series and analytic function as the main content, including its theoretical basis (basic theory of real number, function, measure and limit). It is also a basic course for college mathematics majors. The contents of mathematical analysis include real number, complex number, real function and complex variable function.

Mathematical analysis is developed from calculus. In the modern stage of calculus, it is summarized from applied methods and sublimated into a comprehensive analysis method, and elementary calculus also contains many basic concepts and skills of mathematical analysis. It can be considered that these application methods are the premise of higher calculus. The way of mathematical analysis is related to its geometry, but as long as any mathematical space has a certain neighborhood (topological space) or a certain distance between two objects (metric space), it can be analyzed by mathematical analysis.