  We introduce and motivate the study of quantum spin chains on a
one-dimensional lattice. We classify the varieties of methods that have been
used to study these models into three categories, - a) exact methods to study
specific models b) field theories to describe fluctuations about the classical
ordered phases and c) numerical methods. We then discuss the
$J_1$-$J_2$-$\delta$ model in some detail and end with a few comments on open
problems.
