  This thesis aims to review the cosmological mass function problem, both from
the theoretical and the observational point of view, and to present a new mass
function theory, based on realistic approximations for the dynamics of
gravitational collapse. Chapter 1 gives a general introduction on gravitational
dynamics in cosmological models. Chapter 2 gives a complete review of the mass
function theory. Chapters 3 and 4 present the ``dynamical'' mass function
theory, based on truncated Lagrangian dynamics and on the excursion set
approach. Chapter 5 reviews the observational state-of-the-art and the main
applications of the mass function theories described before. Finally, Chapter 6
gives conclusions and future prospects.
