This chapter mainly introduces the objective functions of GAN. Firstly, a detailed introduction to the standard GAN is provided, including its basic idea, mathematical principles, and algorithm flow, etc. It explains two different objective functions based on f-divergence, namely LSGAN and EBGAN based on the energy model, and also derives and summarizes fGAN based on arbitrary f-divergence. Among another major category of objective functions based on IPM, a very detailed introduction to the Wasserstein distance and the derivation of the objective function of WassersteinGAN is given. Then, a Loss-Sensitive GAN that achieves the same goal as WGAN in a different way is derived. Subsequently, a method WGAN-GP for handling the Lipschitz constraint through a regularization term is introduced. Finally, a detailed explanation of McGAN, MMDGAN, etc. based on the IPM mode will be given. In addition, we explain other types of objective functions, including the reconstruction loss function and the relative loss function.