量子几何张量的实部和虚部均有重要意义，研究二者可以清楚地认识量子系统中的几何与拓扑性质．本文从规范变换作用在实空间上的情况引入，继而延伸到规范变换作用在抽象参数空间上的情况，从而详细地介绍了量子几何张量及一系列概念，加深了对量子几何的进一步理解和认知．

The real and imaginary parts of quantum geometric tensor are of great significance and they can help us to understand the geometric and topological properties of quantum systems clearly. In this paper, from the case of gauge transformation acting on the real space and then extending it to an abstract parametric space, the tensors of quantum geometry with their relevant concepts are introduced in detail, which enable us a further understanding and a deep recognization of quantum geometry for quantum applications.