This book is the second edition of the third volume of Advanced Mathematics compiled by the Mathematics Department of Sichuan University. This edition has made appropriate adjustments to the contents of the first edition and added the answers to the exercises. The main contents of this book are determinant, matrix, linear equations, linear space, linear transformation, Euclidean space, n-ary real quadratic form; Ordinary differential equation; Basic concepts of probability theory, random variables and distribution functions, numerical characteristics of random variables, limit theorems, etc.