The fifth edition of "Lecture Notes on Mathematical Analysis" was written by Liu Yulian, which is a supporting study guide book for "Lecture Notes on Mathematical Analysis". This revision has not changed the writing framework of the original edition, and each section is still written according to the style of the handout. Each section includes five parts: basic content, learning requirements, solution counseling, supplementary examples, and problem solving summary. There are self-test questions at the end of each chapter, and the answers are given at the end of the book. The fifth edition of the Instruction Manual for Learning Mathematical Analysis Textbooks can be used as an instruction manual for mathematics majors, middle school priests, self-taught readers and correspondence students to learn mathematical analysis, and can also be used as a teaching reference book for mathematical analysis exercises and a reference book for postgraduate entrance examination.