We present results of a study of the formation and evolution of the dark matter ( DM ) halos in a COBE -normalized spatially flat \Lambda CDM model ( \Omega _ { 0 } = 1 - \Omega _ { \Lambda } = 0.3 ; h = 0.7 ) .
The dynamics of 256 ^ { 3 } DM particles is followed numerically in a box of 60 h ^ { -1 } Mpc with the dynamic range of 32 , 000 in spatial resolution .
The high resolution of the simulation allows us to examine evolution of both isolated and satellite halos in a representative volume .
We discuss the new halo finding algorithm designed to identify halos in high-density environments , present results on the evolution of velocity function of DM halos and compare it with the Press-Schechter function , discuss the evolution of power spectrum of matter and halo distributions , and mass evolution of halos .

The velocity function of halos at z = 0 compares well with the prediction of the Press-Schechter approximation , but for circular velocities in the range 100 – 200 km/s simulations predict \sim 1.3 time more halos ( mostly in clusters or groups ) .
In real space the power spectra of halos and DM are very different ( halos are anti-biased ) .
Both spectra do not have simple power-law shape .
In redshift space the spectra are close to a power law with \gamma = -2.1 in the range of wave numbers k = 0.2 - 5 h Mpc ^ { -1 } .
The power spectra of halo distribution evolves only mildly for z = 0 - 3 .
The mass evolution of isolated virialized objects determined from the simulation is in good agreement with predictions of the extended Press-Schechter models .
However , satellite halos evolve very different : for some of them the mass decreases with time , which happens if the halos fall into clusters or groups .
We discuss the dependence of the correlation function of halo populations on their environment and merging history .