In this presentation we will explore the connections between quantum
entanglement and symmetry in spin systems. Beginning with the simplest
possible example of two interacting spins, we show how symmetry selects
states that are entangled, or not. A larger system of interacting spins
on a chain is used to illustrate the two roles that symmetry plays: it
constrains interactions between spins and it predicts degeneracies in
the spin states; we also discuss where entanglement occurs in this
system. Lastly, we apply these concepts to pyrochlore magnets.
