The recent emphasis on self assembly processes at the sub-microscopic length scale has been driven both by scientific curiosity and by the promise of significant technological applications. This situation has brought attention to a family of open problems in many-body physics. In particular it highlights the need for methods and results that deserve to be identified as "inverse statistical mechanics". This approach starts by identifying a desirable target structure, then proceeds to construct an interaction potential between particles which causes that structure to self-assemble. Such a construction can serve as a guide for experimental realization (e.g. in colloids).

This lecture surveys the basic concepts and strategies required, and provides a variety of examples of constructed isotropic pair potentials and their corresponding self-assembled structures. These examples include the square and honeycomb crystals in two dimensions, and the simple cubic and diamond crystals in three dimensions. The discussion also covers basic limitations of the inverse statistical mechanical approach.