第一部分介绍我们对量纲理论的创新性看法，引入了“量类”、“单位制族”等若干非常重要的新概念，并以此为基础 对“量纲”一词给出了明确的定义.第二部分在上述创新性理论的基础上给出了Π 定理的严格证明，并举出两例展示了这一定理的巨大威力.

A novel and systematic dimensional analysis is presented. A few new concepts such as “quantity class”and “class of unit systems”are coined, and a clear cut definition of “dimension”is provided. A self-contented proof of the theorem is presented based on these new concepts, and two examples illustrating the great power of the theorem are also given.