  This is a survey on the theory of height zeta functions, written on the
occasion of a French-Japanese winter school, held in Miura (Kanagawa, Japan) in
Jan. 2008. It does not presuppose much knowledge in algebraic geometry. The
last chapter of the survey explains recent results obtained in collaboration
with Yuri Tschinkel concerning asymptotics of volumes of height balls in
analytic geometry over local fields, or in adelic spaces.
