How to Refer to a Greek Manuscript
The proper way to refer to a manuscript in writing is to name the city and the library where it is held, followed (if appropriate) by the collection that it belongs to within the library, and then by its shelfmark, e.g. "Paris, Bibliothèque Nationale de France, Grec 123"; "Oxford, Bodleian Library, Barocci 456"; "Vatican City, Biblioteca Apostolica Vaticana, Vaticano greco 789" (italics are sometimes used for the collections).
This notation is rather cumbersome and, in many contexts, appears redundant and pedantic. As a result, when there is no real risk of confusion, it is common to drastically abbreviate it. There is no real question, for instance, of which manuscript we mean when we write "Vat. gr. 123" (it is, of course, Vatican City, Biblioteca Apostolica Vaticana, Vaticano greco 123), or "Barb. gr. 456" (Vatican City, Biblioteca Apostolica Vaticana, Barberiniano greco 456; there is, indeed, no "Barb." collection in any other library). There is still room for pedantry, however, since the most common way of shortening the name of a manuscript is to refer to it using the Latin demonym of the city where it is kept, e.g. Genavensis (of Geneva); Genuensis (of Genoa); Glascoviensis (of Glasgow), etc. If no library is specified, the largest library in the city is usually referred to; thus "Londin." (Londinensis) refers to the British Library in London; "Monac." (Monacensis) refers to the Bayerische Staatsbibliothek in Munich; "Oxon." (Oxoniensis) refers to the Bodleian Library in Oxford; "Par." or "Paris." (Parisinus) refers to the Bibliothèque Nationale de France in Paris; "Scorial." (Scorialensis) refers to the Real Biblioteca in El Escorial near Madrid; "Vindob." (Vindobonensis) refers to the Österreichische Nationalbibliothek (Austrian National Library) in Vienna (the demonyms are always masculine, because they agree with the word codex, which is understood). When a collection within a library has an official name in a modern language, it is nonetheless customary, in abbreviating a reference to a manuscript, to latinize it (thus "Parisinus graecus 123" is short for "Paris, Bibliothèque Nationale de France, Grec 123", and Vaticanus graecus 456 is short for "Vatican City, Bibiloteca Apostolica Vaticana, Vaticano greco 456").
A few libraries are conventionally referred to by their names in a similar way. Thus, a manuscript kept at the Biblioteca Ambrosiana in Milan is not usually called Mediolanensis but rather Ambros. = Ambrosianus; similarly Laur. = Laurentianus will be a volume in the Biblioteca Medicea Laurenziana in Florence; Marc. = Marcianus will be one in the Biblioteca Nazionale Marciana (or Library of St Mark) in Venice. The abbreviation Pal. gr. (Palatinus graecus) is ambiguous, since it can refer to collections in Heidelberg or in the Vatican (or indeed in Parma, whose main library is also called "Biblioteca Palatina"; however, its volumes are usually referred to as Parmenses); in this pathway it refers to the Vatican collection, unless Heidelb(ergensis) is specified.
The way manuscripts are classified varies a great deal from one library to another, and there is no standard system comparable to the Dewey Decimal System or the Library of Congress Classification for printed books. Many libraries (such as the Biblioteca Medicea Laurenziana in Florence or the Biblioteca Ambrosiana in Milan) still use a traditional, topographical system whereby the individual cabinets or shelving units in which the manuscripts are (or once were) kept are numbered, and the manuscripts are themselves numbered by their position within one of these units: thus, in the Laurenziana, a shelfmark like "Plut. 12.34" means the 34th volume in desk (pluteus) number 12; the cabinets at the Ambrosiana (which are "lettered" rather than numbered) are divided between an upper and a lower section, hence the addition "inf." and "sup." at the end of each shelfmark.
Many libraries have more than one collection within their holdings, either because the volumes are classified by content and/or by language (thus the original collection of the Vatican Library, the "Vaticani", is distinguished into "Vaticani greci", "Vaticani latini", "Vaticani arabi", "Vaticani ebraici", etc.; similarly "Grec", "Latin", etc. at the Bibliothèque Nationale de France; "Phil. gr.", "Theol. gr.", etc. at the Austrian National Library), or because collections which entered a library as a whole have maintained the name of the library they previously belonged to (the collections of the Bodleian Library and of the British Library are mostly named for the person or family who bequeathed, donated or sold them to the library, e.g. the Harley collection, which the British Museum [of which the British Library was then a part] purchased in 1753 from Countess Henrietta Cavendish Harley, or the "Barocci" collection [Barocc. is short for Baroccianus], which was gathered in the sixteenth cntury by Francesco Barozzi and later purchased from his heirs by William Herbert, who donated it to the Bodleian Library in 1629; similarly, the Vatican Library now includes the libraries of the Barberini and Chigi families, which once rivalled the papal collection, among many others). Within each collection, the volumes may simply be numbered (beginning with 1), as the Vaticani greci and the Barberiniani greci are; sometimes the old shelfmarks which refer to the topography of the library of origin are preserved, as with the Vatican Library's Chigi collection, which still bears the shelfmarks referring topographically to the cabinets in the library of the Chigi family.
For some collections, there is more than one possible way of referring to specific volumes: for example, the Vatican Library's Chigiano collection (often latinised to "Chisianus"), which is not ordered by language, has rather odd shelfmarks (as explained above), so when referring to one of the Greek Chigiani, scholars sometimes prefer to refer to P. Franco de' Cavalieri's catalog which describes only the Greek Chigiani and numbers them progressively (thus the manuscript "Chis. R. V. 29" might be referred to as "Chis. gr. 23", since this manuscript received the number 23 in the catalogue). Similarly, Greek manuscripts of the Synodal Collection in Moscow (officially Синодальное собрание рукописей), which are now kept in the State Historical Museum (Государственный исторический музей), are often identified by their number in the catalogue published by the Archimandrite Vladimir in 1894 rather than by their official shelfmarks: thus "Mosq. gr. 117 (Vlad.)" is the same manuscript as "Moscow, State Historical Museum, Sinod. gr. 254".
There is no real convention for referring to manuscripts kept in monasteries in Greece; the important thing is to avoid abbreviating to the point of ambiguity. Thus "Vatop." and "Ivir." clearly refer to the famous Μονὴ Βατοπεδίου and Μονὴ Ἰβήρων on Mount Athos, while "Patm." must refer to the only substantial collection of Greek manuscripts on the island of Patmos, namely that of the Monastery of St. John the Theologian. On the other hand, "Laur.", commonly referring to the Μονὴ Μεγίστης Λαύρας on Mount Athos, could be mistaken for "Laurentianus" (or indeed generically for the word λαύρα, which means "monastery") and is thus best prefixed with "Ath.", as are the names of the lesser-known Athos monasteries such as the Μονὴ Σταυρονικήτα (which you might refer to as "Ath. Stauronic.").
If you have any doubts about which collection is being referred to in an abbreviated notation, or about how to abbreviate your own notation, you will find a very helpful guide in J.-M. Olivier's re-edition of Marcel Richard's Répertoire des bibliothèques et des catalogues de manuscrits grecs (1995, with the two supplement volumes published in 2018), which lists libraries which have Greek manuscripts in their holdings and indicates the published catalogues which describe them.
Another way to discover which collections are held in a library is to use the "Rechercher des manuscrits" page on the Pinakes website (hosted by the Institut de Recherche et d'Histoire des Textes in Paris). If you fill in the "Pays" ("Countries"), "Villes" ("Cities") and "Dépôts" ("Libraries") fields, you will be presented in the "Fonds" field with a drop-down menu of the "collections" which are present in that library (of course you can also use this page for its intended purpose, i.e. to look for information about a specific manuscript!).