The highest achievement of the Greek mathematics is the classification of reguTar solids, the five so-catled Platonic solids, The most compticated sdid is the icosatiedron, Up to and through the 19th century, the most important problem in mathematicss was to toivee algebraic equations In this classic book, Klein showed how to relate these two seamingty unrelated topics and also tied them together with another new theoty of mathematics. hypergaometric functions and monodromy groups. This elearly shows Klein's vision Of the unity of mathematics.This book Inclueds Pefer Slodowy's commentarles and his expository paper on Klein's book to help readers to understand the ADE classification,and their many Unexpected connections and appliations unter current study.