Book excerpt: This book describes the ideal magnetohydrodynamic theory for magnetically conned fusion plasmas. Advanced topics are presented in attempting to fill the gap between the up-to-date research developments and plasma physics textbooks. Nevertheless, they are self contained and trackable with the mathematical treatments detailed and underlying physics explained. Both analytical theories and numerical schemes are given. Besides the current research developments in this field, the future prospects are also discussed. Nowadays, it is believed that, if the ideal MHD theory predicts major instabilities, none of the magnetic confinements of fusion plasmas can survive. The author has also written the book Advanced Tokamak Stability Theory. In view of its importance, the MHD theory is further systematically elaborated in this book. The conventional ideal MHD framework is reviewed together with the newly developed multi-parallel-fluid MHD theory. The MHD equilibrium theory and code are described with the non-letter-'X' separatrix feature pointed out. The continuum modes, quasi-modes, phase mixing, and Alfven resonance heating are analysed. The analytical theories for MHD stability in tokamak configurations are systematically presented, such as the interchange, peeling, ballooning, toroidal Alfven modes, and kink type of modes. The global stability computations are also addressed, including resistive wall modes, error-field amplifications, and Alfven modes, etc.