We consider some general properties of black holes and event horizons, of causality and topology. We define trapped surfaces, congruence, convergence, and show an example of a marginally trapped surface different than the event horizons. We prove the existence of an horizon for de Sitter spacetime, via its Penrose diagram. We then define Rindler spacetime, as the accelerated Minkowski spacetime, that gains an event horizon and mimics what happens for a black hole.