  The present work provides fundamental quantities in generalized elasticity
and dislocation theory of quasicrystals. In a clear and straightforward manner,
the three-dimensional Green tensor of generalized elasticity theory and the
extended displacement vector for an arbitrary extended force are derived. Next,
in the framework of dislocation theory of quasicrystals, the solutions of the
field equations for the extended displacement vector and the extended elastic
distortion tensor are given; that is the generalized Burgers equation for
arbitrary sources and the generalized Mura-Willis formula, respectively.
Moreover, important quantities of the theory of dislocations as the Eshelby
stress tensor, Peach-Koehler force, stress function tensor and the interaction
energy are derived for general dislocations. The application to dislocation
loops gives rise to the generalized Burgers equation, where the displacement
vector can be written as a sum of a line integral plus a purely geometric part.
Finally, using the Green tensor, all other dislocation key-formulas for loops,
known from the theory of anisotropic elasticity, like the Peach-Koehler stress
formula, Mura-Willis equation, Volterra equation, stress function tensor and
the interaction energy are derived for quasicrystals.
