  A general two-dimensional spin model with U$(N)$ invariance, interpolating
between $\CPN$ and ${\rm O}(2N)$ models, is studied in detail in order to
illustrate both the general features of the $1/N$ expansion on the lattice and
the specific techniques devised to extract scaling (field-theoretical)
behavior. The continuum version of the model is carefully analyzed deriving
quantitative $O(1/N)$ physical predictions in order to establish a benchmark
for lattice computations. The $1/N$ expansion on the lattice, including
second-nearest-neighbor interactions, is set up by constructing explicitly
effective propagators and vertices. The technique of asymptotic expansion of
the lattice propagators, basic to the derivation of analytical results in the
scaling domain, is presented in full detail and applied to the model. Physical
quantities, like the free energy and different definitions of correlation
length, are evaluated. The lattice renormalization-group trajectories are
identified and universality among different lattice (and continuum) schemes in
the scaling region is explicitly proven. A review of other developments based
on the lattice $1/N$ expansion is presented.
