  The central objective of this paper is to develop reduced basis methods for
parameter dependent transport dominated problems that are rigorously proven to
exhibit rate-optimal performance when compared with the Kolmogorov $n$-widths
of the solution sets. The central ingredient is the construction of
computationally feasible "tight" surrogates which in turn are based on deriving
a suitable well-conditioned variational formulation for the parameter dependent
problem. The theoretical results are illustrated by numerical experiments for
convection-diffusion and pure transport equations. In particular, the latter
example sheds some light on the smoothness of the dependence of the solutions
on the parameters.
