实分析或实数分析是处理实数及实函数的数学分析。专门研究数列，数列极限，微分，积分及函数串行，以及实函数的连续性，光滑性以及其他相关性质。

实分析常以基础集合论，函数概念定义等等开始。

Real analysis (traditionally, the theory of functions of a real variable) is a branch of mathematical analysis dealing with the real numbers and real-valued functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real numbers, and continuity, smoothness and related properties of real-valued functions.