Since the 19th century, musicologists have been producing complete editions of the music of prominent composers. These serve several purposes: to preserve a composer's work so that it does not vanish; and to provide the most accurate, authoritative edition of those works.
Over the years, the music of prominent composers gets published in many editions. Some of those include additions, deletions, and "corrections" by editors who want to put their own interpretations on the music or to "help" those who don't understand the music. These can include the additions of fingerings, articulations, and tempo marks, and even correcting notes thought to be mistakes by the composer. One of the great things about collected editions is that they try to clear away the misguided efforts of past editors and present the works as close as possible to the form the composer intended. This usually involves comparing several sources (composer's manuscripts, copyist's manuscripts, early editions) and determining what the composer actually wrote. This is called a critical edition. So they tend to be the most reliable versions of many works, and can be referred to if you have a question about whether Mozart really wanted an F sharp in that chord or whether Chopin really connected those two notes with a slur.
Collected editions are often the result of a cooperative effort between a music publisher and a musicological society. For example, the New Bach Edition (Neue Bach Ausgabe) is produced by the Bach Institute in Göttingen, the Bach Archive in Leipzig, and the publisher Bärenreiter.
Most critical editions, including collected editions, come with critical reports that lay out, sometimes measure by measure, why the editors made the decisions they did about notes, articulations, or phrasings. These critical reports are sometimes included in the score, but in the larger sets (e.g. Bach and Mozart), they are issued separately in smaller volumes that are often titled, in German, "Kritische Berichte".
Collected editions are shelved in M3. Like the other items in the RBI, they are for use ONLY in the library. The exception is that the Liszt collected edition is actually in Jones Library, and can be checked out. See the list of collected editions at BW just below this box.
Adam de la Halle
Josquin des Prez
Liszt (in Jones Library)