This EMS volume contains two surveys in the field of partial differential equations. Microlocal analysis is an important method, which many results in the theory of Hamiltonian systems are based on. Another important field is the theory of hyperbolic operators and the Cauchy problem. Egorov and Ivrii give an account of research in these fields and they state unsolved problems. The book is a valuable source of information for graduate students and researchers in the field of partial differential equations and theoretical physics.