  A purely algebraic construction of super-energy tensors for arbitrary fields
is presented in any dimensions. These tensors have good mathematical and
physical properties, and they can be used in any theory having as basic arena
an n-dimensional manifold with a metric of Lorentzian signature. In general,
the completely timelike component of these s-e tensors has the mathematical
features of an energy density: they are positive definite and satisfy the
dominant property. Similarly, the super-momentum vectors have mathematical
properties of s-e flux vectors. The classical Bel-Robinson tensor is included
in our general definition. The energy-momentum and super-energy tensors of
physical fields are also obtained, and the procedure is illustrated by writing
down these tensors explicitly for the cases of scalar, electromagnetic, and
Proca fields. Moreover, `(super)$^k$-energy' tensors are defined and shown to
be meaningful and in agreement for the different physical fields. In flat
spacetimes, they provide infinitely many conserved quantities. In non-flat
spacetimes conserved s-e currents are found for any minimally coupled scalar
field whenever there is a Killing vector. Furthermore, the exchange of
gravitational and electromagnetic super-energy is also shown by studying the
propagation of discontinuities.
