Analyticity, unitarity and scattering amplitudes

The results of local field theory on analyticity properties of scattering amplitudes on the mass shell are reviewed. The following topics are discussed: positivity and enlargement of the analyticity domain; high energy bounds; spin complications and super convergence relations; extension of analyticity and bounds to inelastic reactions; the Pomeranchuk theorem and related questions, vigorous constraints on the pi pi amplitude. (64 refs).