The causal hierarchy of spacetimes

Included in: ESI Lectures in Mathematics and Physics- Recent Developments in Pseudo-Riemannian Geometry The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications of the recently solved ``folk questions on smoothability'', and alternative proposals (as recent isocausality), are also summarized.