The notion of universal enveloping algebra is introduced concerning a commutative Poisson algebra in order to study the category of Poisson modules over the Poisson algebra. The main purpose of this talk is to propose the study of universal enveloping algebra for its own sake. Some basic ring-theoretic and homological properties of the universal enveloping algebra are proved. We also ask some open questions, which suggests us to use universal enveloping algebra to understand the Poisson structure of any commutative algebra.