Alternatives to dark matter: Modified gravity as an alternative to dark
  matter
  The premier alternative to the dark matter paradigm is modified gravity.
Following an introduction to the relevant phenomenology of galaxies, I review
the MOND paradigm, an effective summary of the observations which any theory
must reproduce. A simple nonlinear modified gravity theory does justice to MOND
at the nonrelativistic level, but cannot be elevated to the relativistic level
in a unique way. I go in detail into the covariant tensor-vector-theory (TeVeS)
which not only recovers MOND but can also deal in detail with gravitational
lensing and cosmology. Problems with MOND and TeVeS at the level of clusters of
galaxies are given attention. I also summarize the status of TeVeS cosmology.
