Corrected version of Invariants of orthogonal $G$-modules from the character table. Gabriele Nebe Lehrstuhl B f\"ur Mathematik, RWTH Aachen, Templergraben 64, 52062 Aachen, Germany URL: http://samuel.math.rwth-aachen.de/~LBFM/gabi/ Abstract: Character theoretic methods using Clifford algebras are developed to describe the quadratic forms on a vector space $V$ that are invariant under a finite subgroup of $GL(V)$.