Quantum entanglement rapidly becomes unwieldy to calculate as the number of particles

and the dimension of the spaces associated to those particles increase. One meaningful approach

which simplifies that analysis is the restriction to subsets of states which obey some physically

relevant symmetry. In this thesis, entanglement properties of totally permutation-symmetric,

translationally invariant, and party-site symmetric states are examined, as well as those of small

bond-dimensional matrix product states.