  Thermodynamics of type II superconductors in electromagnetic field based on
the Ginzburg - Landau theory is presented. The Abrikosov flux lattice solution
is derived using an expansion in a parameter characterizing the "distance" to
the superconductor - normal phase transition line. The expansion allows a
systematic improvement of the solution. The phase diagram of the vortex matter
in magnetic field is determined in detail. In the presence of significant
thermal fluctuations on the mesoscopic scale (for example in high $T_{c}$
materials) the vortex crystal melts into a vortex liquid. A quantitative theory
of thermal fluctuations using the lowest Landau level approximation is given.
It allows to determine the melting line and discontinuities at melt, as well as
important characteristics of the vortex liquid state. In the presence of
quenched disorder (pinning) the vortex matter acquires certain "glassy"
properties. The irreversibility line and static properties of the vortex glass
state are studied using the "replica" method. Most of the analytical methods
are introduced and presented in some detail. Various quantitative and
qualitative features are compared to experiments in type II superconductors,
although the use of a rather universal Ginzburg - Landau theory is not
restricted to superconductivity and can be applied with certain adjustments to
other physical systems, for example rotating Bose - Einstein condensate.
