  In the first part of this review paper, the time-dependent Ginzburg-Landau
theory is derived starting from the microscopic BCS model with the help of a
derivative expansion. Special attention is paid to two space dimensions, where
the entire crossover from the weak-coupling BCS limit to the strong-coupling
BEC limit of tightly bound fermion pairs is accessible analytically. The second
part deals with the dual approach to the time-independent Ginzburg-Landau
theory in three space dimensions. In this approach, the magnetic vortices of a
superconductor play the central role, and the superconductor-to-normal phase
transition is understood as a proliferation of these vortices.
