  In my lectures I will deal with three seemingly unrelated problems: i) to
what extent is general relativity exceptional among metric gravity theories?
ii) is it possible to define gravitational energy density applying field-theory
approach to gravity? and iii) can a consistent theory of a gravitationally
interacting spin-two field be developed at all? The connecting link to them is
the concept of a fundamental spin-2 field. A linear spin-2 field encounters
insurmountable inconsistencies when coupled to gravity. After discussing the
inconsistencies of any coupling of the linear spin-2 field to gravity, I
exhibit the origin of the fact that a gauge invariant field has the variational
metric stress tensor which is gauge dependent. I give a general theorem
explaining under what conditions a symmetry of a field Lagrangian becomes also
the symmetry of the stress tensor. It is a conclusion of the theorem that any
attempt to define gravitational energy density in the framework of a field
theory of gravity must fail. Finally I make a very brief introduction to basic
concepts of how a certain kind of a necessarily nonlinear spin-2 field arises
in a natural way from vacuum higher derivative gravity theories. This specific
spin-2 field consistently interacts gravitationally.
