Utility theory as normative decision theory which combines objective measure with subjective psychology and behavior is developed until now that has had a great amount of literature. However, the development of their works were generally partial to a certain aspect, and started from the purpose for their own requirement. The aim of this paper is to introduce utility theory with more systematic, rigorous and synthetic way by mathematical language. This paper consists of four parts: (1) Generation and development of Utility Theory. (2) The mathematical treatment of Utility Theory. (3) Utility Theory of Risk and Insurance. (4) The concluding Remarks.