In order to generalize the Brown-Douglas-Fillmore (BDF) theory to nonstable case,  H. Lin defined a new class of C*-algebra which has continuous scale. A nonunital, $\sigma$-unital, nonelemnetary simple C*-algebra $A$ has continuous scale is equvlent to that its corona algebra $M(A)/A$ is purely infinite and simple. In this talk, we will introduce some background of continuous scale algebra and nonstable extension by ideals with continuous scale, then we will mainly focus on the classification of such extensions.