Abstract
This thesis consists of two parts. In the first part, we will introduce the definition of bivariate Birkhoff interpolation and describe its application on interface problem. Next, we will show an example that how we interpolates a function by compact Birkhoff type interpolation and discuss the property of determinant to help us compute the determinant. In the second part, we will show the data and workable figures of the quadratic, cubic and fourth degree approximation.