Also appears in collection : 2018 - T1 - WS2 - Model theory and valued fields

I plan to survey some of the pleasant properties enjoyed by (topological) dimension of definable sets in the differential field T of transseries; to explain what we know about the the group of automorphisms of T which preserve infinite summation; and to show how these topics are connected. This is joint work with Lou van den Dries and Joris van der Hoeven.