  This paper provides, from one side, a review of the theory of the
cosmological mass function from a theoretical point of view, starting from the
seminal paper of Press & Shechter (1974) to the last developments (Del Popolo &
Gambera (1998, 1999), Sheth & Tormen 1999 (ST), Sheth, Mo & Tormen 2001 (ST1),
Jenkins et al. 2001 (J01), Shet & Tormen 2002 (ST2), Del Popolo 2002a, Yagi et
al. 2004 (YNY)), and from another side some improvements on the multiplicity
function models in literature. ...
