This volume is specially aimed at the graduate student and scientist planning to work or working in the field of accelerator physics. Basic principles of beam dynamics are expanded into the nonlinear regime in order to tackle fundamental problems encountered in present day accelerator design and development. Nonlinear dynamics is discussed both for the transverse phase space to determine chromatic and geometric aberrations which limit the dynamic aperture as well as for the longitude phase space in connection with phase focusing at very small values of the momentum compaction. Whenever possible, effects derived theoretically are compared with observations made at existing accelerators.