I describe the construction of a moduli space for the connected subgroups of an algebraic group, and of a universal family. I give a quick illustration of the notion of universal families, trough Grassmann varieties, then discuss in turn the construction of a moduli space and of a universal family, balancing general statements and examples.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/158