  These lecture notes introduce quantum spin systems and several computational
methods for studying their ground-state and finite-temperature properties.
Symmetry-breaking and critical phenomena are first discussed in the simpler
setting of Monte Carlo studies of classical spin systems, to illustrate
finite-size scaling at continuous and first-order phase transitions. Exact
diagonalization and quantum Monte Carlo (stochastic series expansion)
algorithms and their computer implementations are then discussed in detail.
Applications of the methods are illustrated by results for some of the most
essential models in quantum magnetism, such as the S=1/2 Heisenberg
antiferromagnet in one and two dimensions, as well as extended models useful
for studying quantum phase transitions between antiferromagnetic and
magnetically disordered states.
