  This thesis aims at concluding the classification results for topological
phases with symmetry in 2+1 dimensions. The main result is that topological
phases are classified by a triple of unitary braided fusion categories
$\mathcal E\subset\mathcal C\subset\mathcal M$ plus the chiral central charge
$c$. Here $\mathcal E$ is a symmetric fusion category, $\mathcal
E=\mathrm{Rep}(G)$ for boson systems or $\mathcal E=\mathrm{sRep}(G^f)$ for
fermion systems, consisting of the representations of the symmetry group and
describing the local excitations with symmetry; $\mathcal C$ is the category of
all the quasiparticle excitations in the bulk, containing $\mathcal E$ as its
M\"uger center; $\mathcal M$ is a minimal modular extension of $\mathcal C$,
that also includes the gauged symmetry defects. We also study the stacking of
topological phases with symmetry and two types of anyon condensations based on
such classification.
