  The construction of catalogues of galaxies and the a posteriori study of
galaxy properties in relation to their environment have been hampered by scarce
redshift information. The new 3-dimensional (3D) surveys permit small, faint,
physically bound satellites to be distinguished from a background-projected
galaxy population. We aim to provide representative samples of isolated
galaxies, isolated pairs, and isolated triplets for testing galaxy evolution
and secular processes in low density regions of the local Universe, as well as
to characterise their local and large-scale environments. We used spectroscopic
data from the tenth data release of the SDSS-DR10 to automatically and
homogeneously compile catalogues of 3702 isolated galaxies, 1240 isolated
pairs, and 315 isolated triplets in the local Universe. To quantify the effects
of their local and large-scale environments, we computed the projected density
and the tidal strength for the brightest galaxy in each sample. We find
evidence of isolated pairs and isolated triplets that are physically bound at
projected separations up to $d \leq 450$ kpc with radial velocity difference
$\Delta v \leq 160$ km s$^{-1}$, where the effect of the companion typically
accounts for more than 98% of the total tidal strength affecting the central
galaxy. For galaxies in the catalogues, we provide their positions, redshifts,
and degrees of relation with their physical and large-scale environments. The
catalogues are publicly available to the scientific community. For isolated
galaxies, isolated pairs, and isolated triplets, there is no difference in
their degree of interaction with the large-scale structure, which may suggest
that they have a common origin in their formation and evolution. We find that
most of them belong to the outer parts of filaments, walls, and clusters, and
generally differ from the void population of galaxies.
