  Fundamental properties of the Kosterlitz-Thouless-Berezinskii (KTB)
transition which occurs in systems in the universality class of the
two-dimensional X-Y model are reviewed here with an emphasis on the real-space
renormalization group analysis used to derive the recursion relations. A
derivation of the unique temperature dependence of the correlation length of
this system will be presented and the signatures of the KTB transition in
electronic transport measurements will be explained. Extensions of this model
and technique to layered superconductors will also be presented. The size of
the 3D critical region, the nature of the 3D crossover, and the effect of a
finite electric current will be discussed.
