  I describe in these notes the physical properties of one dimensional
interacting quantum particles. In one dimension the combined effects of
interactions and quantum fluctuations lead to a radically new physics quite
different from the one existing in the higher dimensional world. Although the
general physics and concepts are presented, I focuss in these notes on the
properties of interacting bosons, with a special emphasis on cold atomic
physics in optical lattices. The method of bosonization used to tackle such
problems is presented. It is then used to solve two fundamental problems. The
first one is the action of a periodic potential, leading to a superfluid to
(Mott)-Insulator transition. The second is the action of a random potential
that transforms the superfluid in phase localized by disorder, the Bose glass.
Some discussion of other interesting extensions of these studies is given.
