  We study unconventional superconductivity induced by weak repulsive
interactions in 2D electronic systems at Van Hove singularity (VHS) where
density of states is logarithmically divergent. We define two types of VHS. For
systems at type-I VHS, weak repulsive interactions generically induce
unconventional singlet pairing. However and more interestingly, for type-II VHS
renormalization group (RG) analysis shows that weak repulsive interactions
favor triplet pairing (e.g. p-wave) when the Fermi surface is not sufficiently
nested. For type-II VHS systems respecting tetragonal symmetry, topological
superconductivity (either chiral p+ip pairing or time-reversal invariant $Z_2$
p+ip pairing) occurs generally. We shall also discuss relevance of our study to
materials including recently discovered superconductors LaO$_{1-x}$F$_x$BiS$_2$
which can be tuned to type-II VHS by doping.
