  In this thesis we extend the formalism of tensor network algorithms to
incorporate global internal symmetries. We describe how to both numerically
protect the symmetry and exploit it for computational gain in tensor network
simulations. Our formalism is independent of the details of a specific tensor
network decomposition since the symmetry constraints are imposed at the level
of individual tensors. Moreover, the formalism can be applied to a wide
spectrum of physical symmetries described by any discrete or continuous group
that is compact and reducible. We describe in detail the implementation of the
conservation of total particle number (U(1) symmetry) and of total angular
momentum (SU(2) symmetry). Our formalism can also be readily generalized to
incorporate more exotic symmetries such as conservation of total charge in
anyonic systems.
