Gaussian approximation numbers and metric entropy

The aim of this paper is to survey properties of Gaussian approximation numbers. We state the basic relations between these numbers and and other $s$-numbers as e.g. entropy, approximation or Kolmogorov numbers. Furthermore, we fill a gap and prove new two-sided estimates in the case of operators with values in a $K$-convex Banach space. In a final section we apply the relations between Gaussian and other $s$-numbers to the $d$-dimensional integration operator defined on $L_2[0,1]^d$.