  These are notes for some introductory lectures about microstate geometries
and their construction. The first lecture considers BPS black holes in four
dimensions as a way to introduce what one should expect from the BPS equations.
The second lecture discusses the "no solitons without topology" theorem. The
subsequent lectures move on to the construction and properties of bubbled
microstate geometries in five dimensions. Since these are graduate lectures,
they involve a strongly computational narrative intended to build some
proficiency and understanding of supersymmetric solitons in five-dimensions.
The narrative also regularly "plays tourist" pointing to specific features that
are more general or have broader impact. The last sections contain brief
comments on the larger setting of microstate geometries and describe some of
the more recent developments. These lectures were given as a mini-course at the
IPhT, Saclay in May, 2019.
