  The construction of a theory of quantum gravity is an outstanding problem
that can benefit from better understanding the laws of nature that are expected
to hold in regimes currently inaccessible to experiment. Such fundamental laws
can be found by considering the classical counterparts of a quantum theory. For
example, conservation laws in a quantum theory often stem from conservation
laws of the corresponding classical theory. In order to construct such laws,
this thesis is concerned with the interplay between symmetries and conservation
laws of classical field theories and their application to asymptotically flat
spacetimes.
  This work begins with an explanation of symmetries in field theories with a
focus on variational symmetries and their associated conservation laws.
Boundary conditions for general relativity are then formulated on
three-dimensional asymptotically flat spacetimes at null infinity using the
method of conformal completion. Conserved quantities related to asymptotic
symmetry transformations are derived and their properties are studied. This is
done in a manifestly coordinate independent manner. In a separate step a
coordinate system is introduced, such that the results can be compared to
existing literature. Next, asymptotically flat spacetimes which contain both
future as well as past null infinity are considered. Asymptotic symmetries
occurring at these disjoint regions of three-dimensional asymptotically flat
spacetimes are linked and the corresponding conserved quantities are matched.
Finally, it is shown how asymptotic symmetries lead to the notion of distinct
Minkowski spaces that can be differentiated by conserved quantities.
