Every library should be well organized with well cataloged collections. The Library of Alexandria seems that it was organized so and somehow it laid the foundations of the art of librarianship.
The papyrus rolls or rolled papyri were kept in cabinets or shelves just called βιβλιοθήκαι, bibliothekai. It seems that the rolls or volumes were organized and classified by genre or topics (epic, lyric, tragedy, comedy, philosophy, medicine, rhetoric ...) and within them in alphabetical order of authors and titles. At the upper edge of the roll it was put a label with the "title" of the work (τίτλος in Greek and Latin titulus meaning precisely registration, tag, title,) or index (index, from in– and –dico, to say, provider, announce, communicate, point, mean, etc..)
Callimachus of Cyrene (310-240 BC) was the second official head librarian of the Library and he is considered the "father of the bibliography and librarianship" according as the popular custom of seeking parents for everything.
Callimachus wrote a work called Pinakes or Catalogue of Authors who shone on every single discipline. Pinakes (Greek Πίνακες ) means "table") and is actually a catalog of books in turn consisting of more than 120 books and scrolls. They all volumes of the Library were ranked. From each author it was given a short biography and list of his works with the initials words and reference length; It is reference of this technical qualification in Sumerian, Hittites, Assyrians and Babylonians archives. But alphabetical order is not used
Note: If the library (biblioteka) is the place where you store and display books, , the Pinacotheca, art gallery, from Latin and that from Greek πινακοθήκη and that from Πίνακες,pinakes, table will be the place to keep and display tables or paintings.
He is who creates the classification by keyword and author. Note that it is still used the mechanism to use the initial letters of the author or of title to classify a work. Actually Calímacus does not intended to make an index or catalog of the books in the library, but to create an instrument that would facilitate the work of scholars, given the difficulty of having to unroll papyrus to find its author or its content, because the papyri do not have a front cover or a startup page with the author or the title of the work.
If we apply a broad meaning to “literary genre”, we can consider that they were classified by genres. Six sections for poetry and five for prose were established. Some of the categories were epic, tragic, comic authors, historians, doctors, rhetoricians, laws, miscellaneous; philosophers curiously are missing.
So Demetrius from Phaleras was probably the brain that designed the library using the method of the library of Aristotle, although he not the first official principal.
The first principal was Zenodotus from Ephesus, to which is due the invention of textual criticism by comparing various manuscripts. In an effort to collect the books in your environment, the Library soon found numerous specimens or copies of a work that diverged from each other or not matched exactly or with errors. Zenodotus saw the need to compare them to determine the original text or the closest text and thus invented the "textual criticism". Philologists, in their quest for precision and accuracy, spend their endless efforts to this work. Often even they edit or correct the text in a desire for improvement and perfection of the work; ie the text is considered perfectible but not a sacred text that does not allow the slightest modification.
Another problem which demanded the philological study is the attribution to the many great authors the works that were not theirs, so many writings about medicine were atribued to Hippocrates or books of poems that were not the Iliad or Odyssey to Homer.
Zenodotus prepared critical editions of Hesiod, Pindar and Homer. Each city had its own edition of Homer . It is estimated that Zenodotus could use between 20 and 30 editions of Homer (some are labeled "from cities" and the other "from Museum", referring to their origin in any city or copies performed at the Museum.
This specialist considered that Homer's Iliad and Odyssey were the only works of Homer and he is responsible for the division of the Iliad and Odyssey in 24 chants, as many as the Greek alphabet has letters, the uppercase letters for the Iliad and the lowercase for the Odyssey .
The Alexandrians were generally respectful of the texts and if they had to do some grinding , they did it outside in the scholia (from Lat. Scholium, and this of gr. Σχόλιον, scholion, commentary).
The Alexandrians also divided the work of Herodtus into nine books, each one dedicated to each one of the nine muses.
Diogenes Laertius tells us, for example, about Timon in Book IX, 113:
It is said that Aratus asked him how to get a reliable text of the Homeric poems; he said, 'you will have to find the old copies, and not those that are already corrected'.
Vitruvius tells us in VII, praef. 5-7 how Aristophanes of Byzantium, who knew perfectly the library, discovers the forgers in a poetry competition organized by the king, in which he participated as a judge. As he knew very well the order of the books, he got up from jury , went to the right shelf and returned with the original texts of books that participants wanted to pass off as their own.
See http://www.antiquitatem.com/en/plagiarists-library-of-alexandria-vitruv
This philological work has been essential since the Renaissance attempts to recover the ancient culture. Manuscripts of the Latin works, "superstites", "survivors", result of the copy of the copy of a copy, appear, usually hidden or lost in libraries of monasteries . The errors of copyists, who write by ear, often without understanding what they are transcribing, are accumulated and multiplied. So the criticism of these texts, "textual criticism" is necessary. Otherwise genealogical study of document sets the origin and the way discoursed by the manuscript, now in way of codex or book leaves of animal skin, more manageable than the old papyrus scroll or volume.
These eminent early Alexandrian librarians were succeeded by many other eminent scholars. So Apollonius of Rhodes, author of "The Argonautica", then the mathematician Eratóstones from Cyrene, who measured the circumference of the Earth with impeccable reasoning trigonometric and small precision error, Apollonius of Alexandria, Aristarchus of Samothrace who was the first who established that the Earth revolves around the Sun, Aristophanes of Byzantium, who wrote a "lexicon" of old or unusual words. (Lexicon, from Greek Λεξικός, and this of Lexis, λέξις, word, voice, diction) means collection of words). This same Aristophanes was the first to divide the poetry in verses or kolon (from the Greek κῶλον kolon = member), in stanzas, until he, it is written so followed as prose.
In addition to the scholia or marginal commentaries, they used the footnote on page and various signs of textual criticism, some of them are still used as a horizontal line to mark a suspect spurious verse, the asterisk, as a star for indicate couple or repeated verses, etc.
The Alexandrians therefore created Philology as a science.
Many scholars go through the Library since third century BC to IV century AC , plus the quoted directors said; they are famous, as mathematicians Euclid, Archimedes, Theon of Alexandria, geographers and historians like Manetho, Diodorus and Strabo, botanist as Theophrastus; philosophers as Didymus, Philo of Alexandria and Plotinus; poets as Callimachus and Theocritus and Licofrón; rhetorician as Athanaeus , astronomers and geographers as Strabo and Ptolemy; doctors as Herophilus, Erasistratus and Galen. It is curious that no names of philosophers are cited as such.
How this cast of so many wises should not generate a real attraction and admiration? What current college or academy would not feel so proud and even explode this payroll?
Indeed in Alexandria it was the foundation and basis of Western science and culture.