  In this paper, we study darning of general symmetric Markov processes by
shorting some parts of the state space into singletons. A natural way to
construct such processes is via Dirichlet forms restricted to the function
space whose members take constant values on these collapsing parts. They
include as a special case Brownian motion with darning, which has been studied
in details in \cite{Chen, CF, CFR}. When the initial processes have
discontinuous sample paths, the processes constructed in this paper are the
genuine extensions of those studied in Chen and Fukushima \cite{CF}. We further
show that, up to a time change, these Markov processes with darning can be
approximated in the finite dimensional sense by introducing additional large
intensity jumps among these compact sets to be collapsed into singletons to the
original Markov processes. For diffusion processes, it is also possible to get,
up to a time change, diffusions with darning by increasing the conductance on
these compact sets to infinity. To accomplish these, we extend the semigroup
characterization of Mosco convergence to closed symmetric forms whose domain of
definition may not be dense in the $L^2$-space. The latter is of independent
interest and potentially useful to study convergence of Markov processes having
different state spaces. Indeed, we show in Section 5 of this paper that
Brownian motion in a plane with a very thin flag pole can be approximated by
Brownian motion in the plane with a vertical cylinder whose horizontal motion
on the cylinder is a circular Brownian motion moving at fast speed.
