Papers by the author
The canonical introduction to Cadabra for high-energy physicists is the original paper (now updated for 2.x syntax),
hep-th/0701238 (now updated for 2.x syntax)
A general introduction to Cadabra (the old version, that is) can be found in
Finally, a technical explanation of the motivation for writing this software, as well as a sketch of the internal structure, can be found in the paper
As soon as version 2 reaches a stage where it is feature complete (in the sense that all version 1 algorithms and properties are available), I will put out a new paper.
Leo Brewin has written a nice introduction to Cadabra version 1 for people who intend to use it in General Relativity,
also available as arxiv:0903.2085
The list of papers citing cadabra is getting too long to maintain by hand, but Google Scholar does an excellent job at it. See the list of papers citing the Comp.Phys.Comm. paper and the list of papers citing the hep-th paper.