  Noether's theorem is reviewed with a particular focus on an intermediate step
between global and local gauge and coordinate transformations, namely linear
transformations. We rederive the well known result that global symmetry leads
to charge conservation (Noether's first theorem), and show that linear symmetry
allows for the current to be expressed as a four divergence. Local symmetry
leads to identical conservation of the current and allows for the expression of
the charge as two dimensional surface integral (Noether's second theorem). In
the context of coordinate transformations, an additional step (Poincare
symmetry) is of physical interest and leads to the definition of the symmetric
Belinfante stress-energy tensor, which is then shown to be identically zero in
generally covariant first order theories. The intermediate step of linear
symmetry turns out to be important in general relativity when the customary
first order Lagrangian is used, which is covariant only under affine
transformations. In addition, we derive explicitely the canonical stress-energy
tensor in second order theories in its identically conserved form. Finally, we
analyze the relations between the generators of local transformations, the
corresponding currents and the Hamiltonian constraints.
