During the 21st-century robotics has been growing exponentially owing to the huge influence that robots have in our lives. Therefore, due to my interest in this field, this thesis is going to deal with the construction of a two-wheeled robot and the study of different control methods to balance the robot. A research about control methods will be exposed to let the reader know which control methods are more suitable for our case. Consequently, a mathematical dynamic model of the robot will be represented, this process will allow us to select the ideal methods to control the balancing process. Once the methods will be selected, simulations will be committed to insure that the methods selected behave as they were predicted. Simulations are based on theory that is quite ideal; therefore, to break the ideality of our models and bring them to reality experiments will be performed to confirm if the models control the desired process. Finally, with the simulations' results and experiments, a comparison between the selected methods will be done to chose the best method to achieve the desired robot's behavior.