Local bilinear operators on the lattice and their perturbative renormalisation including O(a) effects

Some basic concepts are discussed to derive renormalisation factors of local lattice operators relevant to deep inelastic structure functions and to other measurable quantities. These $Z$ factors can be used to relate matrix elements measured by lattice techniques to their continuum counterparts. We discuss the $O(a)$ improvement of point and one-link lattice quark operators. Suitable bases of improved operators are derived. Tadpole improvement is applied to get more reliable perturbative results.