Most technical documentation is done directly in the source. A webpage is extracted from these sources every night. The link to this page is available on the left.
The quick starter guide is a document that I update on-the-fly. It is very much hands-on. Peano's fundamental algorithmic ideas were first described in a concise format in the book A Framework for Parallel PDE Solvers on Multiscale Adaptive Cartesian Grids (see picture above). I strongly appreciate if you buy the book, however there's also a download version. More and more recent information is available in an excerpt from my habilitation that you can download for free.
A paper describing the fundamental algorithmic ideas of Peano is
while the arXiv preprint below describes its software architecture/paradigms.
If you search for information how to use Peano in the context or together with other software, please consult the webpages of the respective software (PeanoClaw or ExaHyPE) or have a quick look into the quick start guide (for PETSc).