Self-similarity in general relativity

The different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the 'first' kind, corresponding to spacetimes admitting a homothetic vector. We then survey the various classe s of self-similar solutions to Einstein's field equations and the different mathematical approaches used in studying them. We focus mainly on spatiall y homogenous and spherically symmetric self-similar solutions, emphasizing their possible roles as asymptotic states for more general models. Perfect fluid spherically symmetric similarity solutions have recently been complet ely classified, and we discuss various astrophysical and cosmological appli cations of such solutions. Finally, we consider more general types of self- similar models.