  After a brief discussion of elliptic boundary problems and their properties,
we concentrate on a particular example: the Euclidean Dirac operator in two
dimensions, with its domain determined by local boundary conditions. We discuss
the meromorphic structure of the zeta function of the associated second order
problem, as well as the main characteristic of the first order problem, i.e.,
the boundary contribution to the spectral asymmetry, as defined through the eta
function.
