  We review a geometric approach to classification and examination of quantum
correlations in composite systems. Since quantum information tasks are usually
achieved by manipulating spin and alike systems or, in general, systems with a
finite number of energy levels, classification problems are usually treated in
frames of linear algebra. We proposed to shift the attention to a geometric
description. Treating consistently quantum states as points of a projective
space rather than as vectors in a Hilbert space we were able to apply powerful
methods of differential, symplectic and algebraic geometry to attack the
problem of equivalence of states with respect to the strength of correlations,
or, in other words, to classify them from this point of view. Such
classifications are interpreted as identification of states with `the same
correlations properties' i.e. ones that can be used for the same information
purposes, or, from yet another point of view, states that can be mutually
transformed one to another by specific, experimentally accessible operations.
It is clear that the latter characterization answers the fundamental question
`what can be transformed into what \textit{via} available means?'. Exactly such
an interpretations, i.e, in terms of mutual transformability can be clearly
formulated in terms of actions of specific groups on the space of states and is
the starting point for the proposed methods.
