  In the early seventies, Alan Sandage defined cosmology as the search for two
numbers: Hubble parameter ${{H}_{0}}$ and deceleration parameter ${{q}_{0}}$.
The first of the two basic cosmological parameters (the Hubble parameter)
describes the linear part of the time dependence of the scale factor. Treating
the Universe as a dynamical system it is natural to assume that it is
non-linear: indeed, linearity is nothing more than approximation, while
non-linearity represents the generic case. It is evident that future models of
the Universe must take into account different aspects of its evolution. As soon
as the scale factor is the only dynamical variable, the quantities which
determine its time dependence must be essentially present in all aspects of the
Universe' evolution. Basic characteristics of the cosmological evolution, both
static and dynamical, can be expressed in terms of the parameters ${{H}_{0}}$
and ${{q}_{0}}$. The very parameters (and higher time derivatives of the scale
factor) enable us to construct model-independent kinematics of the cosmological
expansion.
  Time dependence of the scale factor reflects main events in history of the
Universe. Moreover it is the deceleration parameter who dictates the expansion
rate of the Hubble sphere and determines the dynamics of the observable galaxy
number variation: depending on the sign of the deceleration parameter this
number either grows (in the case of decelerated expansion), or we are going to
stay absolutely alone in the cosmos (if the expansion is accelerated).
  The intended purpose of the report is reflected in its title --- "Cosmology
in terms of the deceleration parameter". We would like to show that practically
any aspect of the cosmological evolution is tightly bound to the deceleration
parameter.
