Papers about Cadabra
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)
The Cadabra 2.x software is published as
Cadabra2: computer algebra for field theory revisited
Please cite the two papers above when you use Cadabra in your own work; those citations are the only way to convince the bean counters that this software is useful.
A general introduction to Cadabra (the old version, that is) can be found in
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
A paper describing the new features of version 2 is in preparation and will appear sometime in 2019.
Introductory papers to learn Cadabra
Leo Brewin has written a very thorough new introduction to Cadabra for people who intend to use it in General Relativity, with loads of examples suitable for beginners,
Using Cadabra for tensor computations in General Relativityavailable as arxiv:1912.08839
Also from his hand is a nice paper on how to do Riemann normal coordinate expansions with Cadabra, now updated to use Cadabra2 notation,
Riemann Normal Coordinate expansions using Cadabraavailable as arxiv:0903.2087v2
Research papers citing Cadabra
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.