  On an empirical level, the most successful alternative to dark matter in
bound gravitational systems is the modified Newtonian dynamics, or MOND,
proposed by Milgrom. Here I discuss the attempts to formulate MOND as a
modification of General Relativity. I begin with a summary of the
phenomenological successes of MOND and then discuss the various covariant
theories that have been proposed as a basis for the idea. I show why these
proposals have led inevitably to a multi-field theory. I describe in some
detail TeVeS, the tensor-vector-scalar theory proposed by Bekenstein, and
discuss its successes and shortcomings. This lecture is primarily pedagogical
and directed to those with some, but not a deep, background in General
Relativity
