This text gives a systematic presentation of the global classical solution and the global classical discontinuous solution to quasilinear hyperbolic systems. The greater part of the book is the result of academic research on the part of the author and his collaborators, dealing with the Cauchy problem, boundary value problems, free boundary problems and the generalized Riemann problem. Some material contained in the book is being published for the first time, and what was previously published in the form of separate papers has also been revised and updated.