  In this paper, we present an adaptive hybridizable $C^0$ discontinuous
Galerkin (HCDG) method for Kirchhoff plates. A reliable and efficient a
posteriori error estimator is produced for this HCDG method.
Quasi-orthogonality and discrete reliability are established with the help of a
postprocessed bending moment and the discrete Helmholtz decomposition. Based on
these, the contraction property between two consecutive loops and complexity of
the adaptive HCDG method are studied thoroughly. The key points in our analysis
are a postprocessed normal-normal continuous bending moment from the HCDG
method solution and a lifting of jump residuals from inter-element boundaries
to element interiors.
