Short answers, pulled from the story.
Inscriptiones Latinae Selectae is a three-volume selection of Latin inscriptions edited by Hermann Dessau and published in Berlin between 1892 and 1916. It is standardly abbreviated ILS and is also cited as Dessau or D.
Inscriptiones Latinae Selectae contains inscriptions numbered from ILS 1 to ILS 9522, with the third volume also including an index. The collection was issued in five parts across three volumes.
The inscriptions are grouped by topic within thematic chapters called capita (singular caput). Categories include funerary inscriptions and inscriptions pertaining to collegia. Each inscription carries its own identifying number.
Scholars typically give both references together, for example CIL 12.2.774 paired with ILS 39. A concordance linking the two corpora was published in Rome in 1950 and in Berlin in 1955.
The work was published serially from 1892 to 1916 and has been reprinted numerous times. All three volumes are available as full-text downloads from the Internet Archive, and the collection is searchable through the Epigraphik-Datenbank Clauss/Slaby under the abbreviation D.
All supporting material and notes in Inscriptiones Latinae Selectae are written in Latin, the shared scholarly language that allowed researchers across different countries to use the same apparatus.