  We present algebraic multilevel iteration (AMLI) methods for isogeometric
discretization of scalar second order elliptic problems. The construction of
coarse grid operators and hierarchical complementary operators are given.
Moreover, for a uniform mesh on a unit interval, the explicit representation of
B-spline basis functions for a fixed mesh size $h$ is given for $p=2,3,4$ and
for $C^{0}$- and $C^{p-1}$-continuity. The presented methods show $h$- and
(almost) $p$-independent convergence rates. Supporting numerical results for
convergence factor and iterations count for AMLI cycles ($V$-, linear $W$-,
nonlinear $W$-) are provided. Numerical tests are performed, in two-dimensions
on square domain and quarter annulus, and in three-dimensions on quarter thick
ring.
