  In this article we give a unified treatment of the construction of all
possible Weitzenb\"ock formulas for all irreducible, non--symmetric holonomy
groups. The resulting classification is two--fold, we construct explicitly a
basis of the space of Weitzenb\"ock formulas on the one hand and characterize
Weitzenb\"ock formulas as eigenvectors for an explicitly known matrix on the
other. Both classifications allow us to find tailor--suit Weitzenb\"ock
formulas for applications like eigenvalue estimates or Betti number estimates.
