"Advanced Mathematics" is compiled according to "Basic Requirements of Basic Mathematics Course Teaching for Engineering Undergraduates" formulated by the Teaching Guidance Sub-committee of Basic Mathematics Course for Non-mathematics Majors of the Ministry of Education. Contents include: function and limit, unary function calculus, vector algebra and spatial analytic geometry, multivariate function calculus, series, ordinary differential equations, etc. At the end of the book, there are several commonly used plane curves and their equations, three appendices such as integral table and preliminary field theory, as well as reference answers to exercises. This book describes the basic concepts clearly and accurately, discusses the basic theories concisely and easily, and has a variety of examples and exercises, emphasizing the cultivation of basic computing ability and the practical application of theories. This book can be used as a teaching material for engineering undergraduates in colleges and universities, as well as a teaching reference book for teachers and a self-taught advanced mathematics course.