Infi nite hierarchies of awareness and belief arise in games with unawareness, similarly to belief hierarchies in standard games. A natural question is whether each hierarchy describes the player's awareness of the hierarchies of other players and beliefs over these, or whether the reasoning can continue indefinitely. This paper constructs the universal type space with unawareness where each type has an awareness level and a belief over types. Countable hierarchies are therefore sufficient to describe all uncertainty in games with unawareness.