  Shape dynamics is a completely background-independent universal framework of
dynamical theories from which all absolute elements have been eliminated. For
particles, only the variables that describe the shapes of the instantaneous
particle configurations are dynamical. In the case of Riemannian
three-geometries, the only dynamical variables are the parts of the metric that
determine angles. The local scale factor plays no role. This leads to a
shape-dynamic theory of gravity in which the four-dimensional diffeomorphism
invariance of general relativity is replaced by three-dimensional
diffeomorphism invariance and three-dimensional conformal invariance. Despite
this difference of symmetry groups, it is remarkable that the predictions of
the two theories -- shape dynamics and general relativity -- agree on spacetime
foliations by hypersurfaces of constant mean extrinsic curvature. However, the
two theories are distinct, with shape dynamics having a much more restrictive
set of solutions. There are indications that the symmetry group of shape
dynamics makes it more amenable to quantization and thus to the creation of
quantum gravity. This introduction presents in simple terms the arguments for
shape dynamics, its implementation techniques, and a survey of existing
results.
