In this book, the problems with respect to the construction of the Fractal Interpolation Function and its application in the affine fractal sets are studied.Today, under the interests of many scholars, the research on the fractal theory has been developed deeply and fractal has most applications in the field of nature and society.The graph of the fractal interpolation function becomes the attractor against any Iterated Function System so IFS is a powerful mean to generate and analyze the new fractal interpolation function.It is the most important problem in fractal interpolation theory to generate new fractal interpolation functions and study its properties.This book contains five chapters. We think that this book will present great interests to the researchers in the natural and applied sciences and attract a very surprising attention of the scholars in the fractal theory field, and we think that our results in this book become advances in the fractal interpolation theory.