  We have learnt in the last decades that the majority of galaxies belong to
high density regions interconnected in a sponge-like fashion. This large-scale
structure is characterised by clusters, filaments, walls, where most galaxies
concentrate, but also under-dense regions, called voids. The void regions and
the galaxies within represent an ideal place for the study of galaxy formation
and evolution as they are largely unaffected by the complex physical processes
that transform galaxies in high-density environments. These void galaxies can
hold the key as well to answer current challenges to the $\Lambda$CDM paradigm.
The Calar Alto Void Integral-field Treasury surveY (CAVITY) is a Legacy project
approved by the Calar Alto Observatory to obtain spatially resolved
spectroscopic information of $\sim300$ void galaxies in the Local Universe
(0.005 < z < 0.050) covering from -17.0 to -21.5 in $\rm r$ band absolute
magnitude. It officially started in January 2021 and has been awarded 110
useful dark observing nights at the 3.5 m telescope using the PMAS
spectrograph. Complementary follow-up projects including deep optical imaging,
integrated, as well as resolved CO data, and integrated HI spectra, have joint
the PMAS observations and naturally complete the scientific aim of
characterising galaxies in cosmic voids. The extension data has been
denominated CAVITY+. The data will be available to the whole community in
different data releases, the first of which is planned for July 2024, and it
will provide the community with PMAS data cubes for around 100 void galaxies
through a user friendly, and well documented, database platform. We present
here the survey, sample selection, data reduction, quality control schemes,
science goals, and some examples of the scientific power of the CAVITY and
CAVITY+ data.
