We consider an arbitrary linear elliptic first--order differential operator A with smooth coefficients acting on sections of a complex vector bundle E over a compact smooth manifold M with smooth boundary. We describe the analytic and topological properties of A in a collar neighborhood U of the boundary and analyze various ways of writing A|U in product form; we discuss the sectorial projections of the corresponding tangential operator; construct various invertible doubles of A by suitable local boundary conditions; obtain Poisson type operators with different mapping properties; and provide a canonical construction of the Calderon projection. We apply our construction to generalize the Cobordism Theorem and to determine sufficient conditions for continuous variation of the Calderon projection and of well--posed self-adjoint Fredholm extensions under continuous variation of the data.