In this scenario structure grows hierarchically by gravitational instability of small density perturbations present at early times. Small scale structures collapse first and then merge into more massive systems, a highly nonlinear process that is best followed with direct numerical simulations. Once the spectrum of density fluctuations and the cosmological parameters have been specified, the evolution of the collisionless dark matter component can be followed in detail using standard N-body techniques. Explicit inclusion of the observable component of the universe (gas and stars) requires, on the other hand, solving the equations which govern the evolution of a collisional fluid, including the many additional physical processes which influence its structure: star formation and evolution; energy input from stellar winds, stellar radiation, and supernova explosions; ionization effects from stellar and QSO radiation fields; heavy element enrichment; heat conduction; and magnetic fields.
Only recently have developments in computer hardware and software made hydrodynamical codes useful tools in studies of the hydrodynamics of the formation of extragalactic systems. Grid-based Eulerian codes and Lagrangian schemes based on the Smooth Particle Hydrodynamics (SPH) technique have both become available in the past 5 years, and have already improved dramatically our understanding of the process of formation and evolution of galaxies, galaxy clusters, the large scale structure and QSO absorption line systems. I have participated actively in these efforts, and have developed a fully Lagrangian, N-body/hydro code especially designed to evolve a mixture of collisional and collisionless fluids in three dimensions. It is based on the Smooth Particle Hydrodynamics technique and uses a nearest-neighbour binary tree to compute gravitational forces. It is free from symmetry restrictions and has a large dynamic range through the use of individual timesteps andsmoothing lengths. This code has been thoroughly tested and has already been applied to a number of problems related to the formation and evolution of galaxies and galaxy clusters in hierarchically clustering universes. In the sections that follow I describe some of the results of my previous work, and outline how I intend to build upon them to address a number of unresolved questions regarding the formation and evolution of extragalactic systems.