  Quasinormal modes are eigenmodes of dissipative systems. Perturbations of
classical gravitational backgrounds involving black holes or branes naturally
lead to quasinormal modes. The analysis and classification of the quasinormal
spectra requires solving non-Hermitian eigenvalue problems for the associated
linear differential equations. Within the recently developed gauge-gravity
duality, these modes serve as an important tool for determining the
near-equilibrium properties of strongly coupled quantum field theories, in
particular their transport coefficients, such as viscosity, conductivity and
diffusion constants. In astrophysics, the detection of quasinormal modes in
gravitational wave experiments would allow precise measurements of the mass and
spin of black holes as well as new tests of general relativity. This review is
meant as an introduction to the subject, with a focus on the recent
developments in the field.
