1. 中文简介 本课程是数学专业研究生的必修课之一，是数学分析、高等代数、实变函数等基础课程的后继课程，是研究生学习的基础。泛函分析是研究线性空间到拓扑线性空间之间满足各种拓扑和代数条件的映射的分支学科，包括算子理论、空间理论、非线性分析等，并在众多学科领域，如微分方程、概率论、量子理论等得到广泛应用。它综合地运用分析、代数和几何的观点、方法研究分析数学中的许多问题，是讲具体的分析问题抽象到一种更加纯粹的代数拓扑结构的形式中进行的研究。该课程是学习其他数学分支与科研工作的重要基础。 2. 英文简介 This course is one of the required courses for graduate students majoring in mathematics. It is a follow-up course of basic courses such as mathematical analysis, advanced algebra and real change function. Functional analysis is a branch subject that studies the mapping between linear space and topological linear space that satisfies various topological and algebraic conditions, including operator theory, spatial theory, nonlinear analysis, etc., and has been widely applied in many fields, such as differential equations, probability theory, quantum theory, etc. It comprehensively uses analysis, algebraic and geometric perspectives and methods to study and analyze many problems in mathematics. It is a study that abstracts specific analysis problems into a more pure form of algebraic topology. This course is an important foundation for learning other branches of mathematics and scientific research.