  We elaborate a new method for constructing traces of quadratic forms in the
framework of Hilbert and Dirichlet spaces. Our method relies on monotone
convergence of quadratic forms and the canonical decomposition into regular and
singular part. We give various situations where the trace can be described more
explicitly and compute it for some illustrating examples. We then show that
Mosco convergence of Dirichlet forms implies Mosco convergence of a subsequence
of their approximating traces and that asymptotic compactness of Dirichlet
forms yields asymptotic compactness of their traces.
