Although the application of reproducing kernel has been explored in different fields in the past twenty to thirty years and the relevant researches are active in the recent five years, there is still not a book on the application of reproducing kernel. This book attempts to introduce to the readers engaged in mathematical application these solutions, especially the constructing theory of the reproducing kernel space that the authors originally created and gradually improved. Reproducing kernel space is a special Hilbert space. the authors have been engaged in the constructing theory research of the reproducing kernel space since 1980's, and worked out a series of specific structural methods for reproducing kernel space and reproducing kernel functions.