The study of the mechanisms that govern origin and propagation of stellar jets involves the treatment of many concurrent physical processes such as gravitation, hydrodynamics and magnetohydrodynamics, atomic physics and radiation. In the past years, an intensive work has been done looking for so- tions of the ideal MHD equations in the steady state limit as well as studying the stability of out?ows in the linear regime. These kind, of approaches have provided a contribution to the understanding of jets that can hardly be ov- estimated. However, the extension of the analyses to the time-dependent and nonlinear regimes could not be avoided, and the MHD numerical simulations were the only mean to achieve this goal. Intherecentyears,considerableprogresseshavebeenmadebythecom- tational?uiddynamiccommunityinthedevelopmentofnumericaltechniques, theso-calledhighresolutionshockcapturingschemes,wellsuitedforthetre- ment of supersonic ?ows with discontinuities. The numerical simulations of astrophysical jets took advantage of these developments; however new physics needed to be incorporated, such as magnetic ?eld e?ects, radiation losses by diluted gases, and proper astrophysics environments. These needs led to the nontrivial extension of the methods devised for the Euler equations of g- dynamics to the magneto-hydrodynamical system. On the other hand, the possibility of carrying out numerical calculations has been greatly facilitated bytheavailability, ononehand,ofpowerfulsupercomputersand,ontheother hand, of fast processors at low cost. Large scale 3D simulations of jets at high resolution are now possible thanks to supercomputers, but also high reso- tion 2D MHD simulations can be performed routinely on desktop computers.

These proceedings are the result of a three-day meeting held in Oogliani (Italy), on October 2-4 2003, whose title was "VIrtual Astrophysical Jets 2003". Our goal in convening this meeting was to gather some of the scientists among the most active in the field of numerical simulations and modelling of astrophysi cal jets. For keeping the participants close to the "real world", we also invited a few observers to give up-to-date reviews outlining the state-of-the-art of jet observations. The principal aim of the meeting was thus to present and critically discuss the state-of-the-art numerical simulations, analytical models and laboratory ex periments for reproducing the main aspects of astrophysical jets and compar ing them with observations. The discussion has been focused on the following topics: * Observations and intepretions of jets from young stars and AGNs, comparisons of models with observations; * MHO accelerations of jets: steady self-similar models, MHO numerical simula tions of time-dependent accelerations mechanisms; * Jet stability and interaction with the ambient: formation of knots in YSO jets, jet survival to instabilities, deceleration of relativistic jets in FRI sources, simulations of jets-IGM interactions, jets propagation and galaxy formation; * Numerical codes and their validation: relativistic MHO codes, comparisons among different numerical schemes, jets in the laboratory and code validation. These topics have been discussed intensively during the meeting, and the out come of these discussions is presented in this volume. The contributions have been divided in five sections.