  Temporal variability in flux and spectral shape is ubiquitous in the X-ray
sky and carries crucial information about the nature and emission physics of
the sources. The EPIC instrument on board the XMM-Newton observatory is the
most powerful tool for studying variability even in faint sources. Each day, it
collects a large amount of information about hundreds of new serendipitous
sources, but the resulting huge (and growing) dataset is largely unexplored in
the time domain. The project called Exploring the X-ray transient and variable
sky (EXTraS) systematically extracted all temporal domain information in the
XMM-Newton archive. This included a search and characterisation of variability,
both periodic and aperiodic, in hundreds of thousands of sources spanning more
than eight orders of magnitude in timescale and six orders of magnitude in
flux, and a search for fast transients that were missed by standard image
analysis. All results, products, and software tools have been released to the
community in a public archive. A science gateway has also been implemented to
allow users to run the EXTraS analysis remotely on recent XMM datasets. We give
details on the new algorithms that were designed and implemented to perform all
steps of EPIC data analysis, including data preparation, source and background
modelling, generation of time series and power spectra, and search for and
characterisation of different types of variabilities. We describe our results
and products and give information about their basic statistical properties and
advice on their usage. We also describe available online resources. The EXTraS
database of results and its ancillary products is a rich resource for any kind
of investigation in almost all fields of astrophysics. Algorithms and lessons
learnt from our project are also a very useful reference for any current and
future experiment in the time domain.
