As the large amount of sequencing data accumulated in past decades and it is still accumulating, we need to handle the more and more sequencing data. As the fast development of the computing technologies, we now can handle a large amount of data by a reasonable of time using the neural network based model. This tutorial will introduce the the mathematical model of the single cell variational inference (scVI), which use the variational auto-encoder (building on the neural networks) to learn the distribution of the data to gain insights. It was written for beginners in the simple and intuitive way with many deduction details to encourage more researchers into this field.