According to physical cosmology the Universe began from a singularity (very hot and dense point) about 13.8 Gyrs ago. But we see structures in all scales from planets and stars to large super clusters and voids. The dilemma is: *“How these structures formed and evolved from a singularity?”. *There are many questions about the roles of dark matter and dark energy in structure formation.

- Hierarchical clustering

Theoretical and observational data on galaxy clustering suggest that there is a hierarchy in structure formation that starts with early, low massive objects and finishes with late, massive ones, these later arising from the gravitational clustering of the former.

It is generally believed that the first objects, as well as their subsequent clusterings, have their origin in small amplitude density inhomogeneities which have grown by gravitational instability as the universe expanded. The evolution of density inhomogeneities passes through two distinct stages:

- linear regime: the perturbation expands while its small amplitude increases. Owing to the independence of the Fourier modes the set of equations governing the amplitude evolution can be solved analytically.
- non-linear regime: for high amplitudes the perturbation begins to collapse and finally virializes giving rise to a newborn object. In this regime the Fourier modes are coupled together and the only accurate way to follow the evolution of perturbations is by means of numerical simulations.

Alternatively, theoretical models can also be used to deal with the non-linear regime. __Press & Schechter (1974; PS)__proposed an innovative method, founded on features of the linear density field, capable of giving the mass distribution of collapsed objects. The fact that the predicted mass function fits those from N-body simulations suggests the capability of the PS formalism to describe the real clustering process. This formalism has been extended (__Lacey & Cole 1993__) to allow the calculation of some interesting quantities related to the growth history of collapsed objects, such as the merger and accretion rates and the survival and formation times, which complete the gravitational clustering view.

Hereis a pedagogical paper to learn basics of *theory of cosmological structure formation.*