This course introduces students to elementary real analysis, which makes what the students have learned from calculus courses rigorous. The following topics will be covered: the properties of real numbers, sequences, sets of real numbers, continuous functions, the integral, sequences and series of functions, power series, the Euclidean spaces Rn. In this course, students will learn various facts and practice computing limits and integrals to solve specific problems, which helps students deeply understand and apply the knowledge in calculus class. In addition, instructing students how to read and write proofs is another essential goal of this course.