The isomorphism relation of non-Archimedean Polish groups‎‎.

Kechris, Nies and Tent proposed a program to study the isomorphism relation of Borel classes of non-Archimedean Polish groups and to determine their exact complexity in the Borel reducibility hierarchy. In this minicourse I will give a survey of the known results in this program, including some recent work on isometry groups of countable Urysohn-type spaces, extremely amenable groups and procountable groups.