Control is the core of all scientific issues.Mathematical models are the basis of all control problems.The movement law of things described by equations is the mathematical model.The development of different disciplines is to establish the process of their mathematical models.This paper divides the mathematical models of the linear dynamic systems into three categories:the timeseries models,the equation error type models and the output error type models,and introduces basic mathematical models of linear systems in detail,including the discretization of continuoustime system models and model equivalence transform,singleinput singleoutput stochastic system,multivariable systems,multivariablelike systems,multipleinput and multipleoutput systems such as the main model,submodel and subsubmodel of the transfer function matrix,multipleinput singleoutput systems,and singleinput multipleoutput systems.