This master thesis is aimed at single auv (autonomous underwater vehicle) and auv formation control in two-dimensional horizontal plane. For sake of increasing services life and saving communication resources, event-triggered mechanism is taken into consideration. two coordinate systems are introduced: earth-fixed frame and body-fixed frame. Some motion parameters and force analysis are used in the process of establishing mathematical model. then the related theorems, lemmas and control method commonly used in analyzing control systems are introduced. then, the auv control system is divided into two subsystems with cascade relationship. considering each subsystem separately, a controller is designed that can simultaneously carry out trajectory tracking and point stabilization. considering the service life of actuator equipment, an event-triggered controller was designed, which can reduce the frequency of actuator adjustment, prolong the service life of equipment. finally, combining the idea of light-of-sight method and virtual structure method, the auv formation tracking control problem is solved similarly to single auv. in deep sea conditions, an event- triggered communicating mechanism is designed to reduce the frequency of communication and adapt to limited communication resources, which balances the reliability and economy. matlab simulink is used to simulate the controller designed in the thesis, and confirms the feasibility of the controller.