  We study multivariate problems like function approximation, numerical
integration, global optimization and dispersion. We obtain new results on the
information complexity $n(\varepsilon,d)$ of these problems. The information
complexity is the amount of information (e.g. the number of function values)
that is needed to solve the $d$-dimensional problem up to a prescribed error
$\varepsilon>0$. We present optimal algorithms for some of these problems.
  An extended abstract can be found in the section "Introduction and Results".
