the subgroup growth of a group is the study of the number of its index n subgroups as a function of n. we will present some sharp estimates on this growth for lattices l in higher rank semi-simple lie groups g. a surprising phenomenom is that this growth depends only on the root system of g and not on l. in the most general case, the results depend on the generalized riemann hyphothesis but a number of results can be also proved unconditionally.