  These are the notes for a series of lectures given on the theory of canonical
and crystal bases for Hall algebras (for a summer school in Grenoble in 2008).
It may be viewed as a follow-up to arXiv:math/0611617. It covers the
construction, due to Lusztig, of the canonical bases for the Hall algebra of a
quiver Q in terms of a certain category of perverse sheaves over the moduli
space of representations of Q. It also contains an exposition of Kashiwara and
Saito's geometric construction of the crystal graph in terms of irreducible
components of Lusztig's lagrangian in the cotangent bundle to the above moduli
spaces. The last section deals with the Hall algebras of curves. It contains a
few new results and conjectures. Apart from these, the text is purely
expositional.

Quantum Algebra;Representation Theory