  This manuscript is a survey on results related to boundary layers and the
vanishing viscosity limit for incompressible flow. It is the lecture notes for
a 10 hour minicourse given at the Morningside Center, Academia Sinica, Beijing,
PRC from 11/28 to 12/07, 2007. The main topics covered are: a derivation of
Prandtl's boundary layer equation; an outline of the rigorous theory of
Prandtl's equation, without proofs; Kato's criterion for the vanishing
viscosity limit; the vanishing viscosity limit with Navier friction condition;
rigorous boundary layer theory for the Navier friction condition and boundary
layers for flows in a rotating cylinder.
