This paper investigates the mass function of dark matter halos in a large set of cosmological simulations of flat ΛCDM cosmology, focusing on their evolution up to \( z \leq 2 \). The halos are identified as isolated density peaks and their masses are measured within radii enclosing specific overdensities. The authors argue that spherical overdensity masses are more directly linked to cluster observables compared to masses measured using the friends-of-friends (FOF) algorithm, making them more suitable for accurate forecasts of halo abundances. They calibrate the mass function at \( z = 0 \) for virial masses ranging from \( 10^{11} h^{-1} M_{\odot} \) to \( 10^{15} h^{-1} M_{\odot} \) to within 5%. Fitting functions for the halo mass function are derived for a wide range of overdensities at \( z = 0 \) and earlier epochs. The main finding is that the mass function cannot be represented by a universal fitting function at this level of accuracy, with the amplitude of the "universal" function decreasing monotonically by approximately 20-50% from \( z = 0 \) to \( z = 2.5 \). Additionally, evidence for redshift evolution in the overall shape of the mass function is found. The paper discusses the implications of these findings for the calibration of halo mass functions in observational studies and the interpretation of cluster observables.This paper investigates the mass function of dark matter halos in a large set of cosmological simulations of flat ΛCDM cosmology, focusing on their evolution up to \( z \leq 2 \). The halos are identified as isolated density peaks and their masses are measured within radii enclosing specific overdensities. The authors argue that spherical overdensity masses are more directly linked to cluster observables compared to masses measured using the friends-of-friends (FOF) algorithm, making them more suitable for accurate forecasts of halo abundances. They calibrate the mass function at \( z = 0 \) for virial masses ranging from \( 10^{11} h^{-1} M_{\odot} \) to \( 10^{15} h^{-1} M_{\odot} \) to within 5%. Fitting functions for the halo mass function are derived for a wide range of overdensities at \( z = 0 \) and earlier epochs. The main finding is that the mass function cannot be represented by a universal fitting function at this level of accuracy, with the amplitude of the "universal" function decreasing monotonically by approximately 20-50% from \( z = 0 \) to \( z = 2.5 \). Additionally, evidence for redshift evolution in the overall shape of the mass function is found. The paper discusses the implications of these findings for the calibration of halo mass functions in observational studies and the interpretation of cluster observables.