  This is an introduction to conformal invariance and two-dimensional critical
phenomena for graduate students and condensed-matter physicists. After
explaining the algebraic foundations of conformal invariance, numerical methods
and their application to the Ising, Potts, Ashkin-Teller and XY models,
tricritical behaviour, the Yang-Lee singularity and the XXZ chain are
presented. Finite-size scaling techniques and their conformal extensions are
treated in detail. The vicinity of the critical point is studied using the
exact $S$-matrix approach, the truncation method, the thermodynamic Bethe
ansatz and asymptotic finite-size scaling functions. The integrability of the
two-dimensional Ising model in a magnetic field is also dealt with. Finally,
the extension of conformal invariance to surface critical phenomena is
described and an outlook towards possible applications in critical dynamics is
given.
