AppleScript libraries were introduced along with AppleScriptObjective-C, in Mavericks (OSX 10.9). The AppleScript Language Reference has this chapter on script libraries (also on p. 72 of the pdf):

https://developer.apple.com/library/mac/documentation/AppleScript/Conceptual/AppleScriptLangGuide/conceptual/ASLR_script_objects.html#//apple_ref/doc/uid/TP40000983-CH207-SW6

MacOsxAutomation explains libraries in simpler terms:

https://macosxautomation.com/mavericks/libraries/

MacScripter also has a tutorial:

http://macscripter.net/viewtopic.php?id=41638

Chris Page says a few things about script library caching:

http://lists.apple.com/archives/applescript-users/2016/Jan/msg00031.html

Although it is not strictly related to AppleScript libraries, the AppleScript Reference Library caters to the AppleScript developers and as such is an invaluable ressource:

https://applescriptlibrary.wordpress.com

(alphabetical order of author)

Apple Configurator 2 provides users with a library inside its /Contents/Library/Script Libraries/ folder. The application itself is not scriptable. As Shane Stanley explains on the Apple Script list, the handlers are built around command line tools via do shell script.(1) The application is available from the App Store only.

https://support.apple.com/en-ap/HT205285

(1) http://lists.apple.com/archives/applescript-users/2015/Oct/msg00032.html

applescript-stdlib is an attempt at writing a standard library for AppleScript.(1) It proposes handlers for dates, files, formats, library support, lists, maths, tasks, tests, text and types.

https://github.com/hhas/applescript-stdlib

(1) http://lists.apple.com/archives/applescript-users/2016/Jan/msg00042.html

SmartString is a string manipulation library, "based on a 1984 Scientific American article by Niklaus Wirth about a better way to manipulate strings" (1).

http://www.seanet.com/~jonpugh/software/SmartString.applescript

(1) Quoted from Jon's mail to the AS list on December 21 2015

Lukas has a nice collection of libraries either written by himself or copied from the net. They offer handlers for display, files & folders, iWorks, Keychain, lists, numbers, property lists, strings, Time Machine, and urls.

http://applescript.bratis-lover.net/library/

The disk image for UI Browser includes the PFiddlesoft GUI Scripting Library that offers handlers useful in GUI Scripting scripts. The library can be used independently of UI Browser.

http://pfiddlesoft.com/uibrowser/

Shane is consolidating the various libraries he provides at the following link:

http://www.macosxautomation.com/applescript/apps/Script_Libs.html

At the time of writing, the link gives access to:

• BridgePlus (collection of handlers based on the functionality of ASObjC Runner.app, and commands that support improved bridging between AppleScript and Cocoa)
• CalendarLib (script library for manipulating calendar events without using Calendar.app)
• CalendarLib EC (identical to CalendarLib except it requires El Capitan or later and does not require BridgePlus)
• DefaultsLib (makes it simple to take advantage of the built-in defaults system for storing your scripts' preferences)
• Dialog Toolkit (script library for showing enhanced dialogs)
• FileTagsLib (to retrieve and set file tags)
• FileManagerLib (provides handlers for file management tasks like duplicating, copying, moving, renaming, deleting, and trashing files, etc.)

Shane also posted three sample libraries to the AppleScript list in December 2013. "All were based on an object-oriented design shamelessly borrowed from SmartString, down to the names." (1) The code will eventually be consolidated on Shane's page, but I'm putting the links here in the meanwhile.

Smartset (One of the useful classes in Cocoa (and other languages) is the set, which is like a list except each item can only appear once. Sets are not normally ordered like lists, but Cocoa also has ordered lists, which maintain their order. Anyway, they are a good class to show the convenience of using ASObjC-based script libraries.) http://lists.apple.com/archives/applescript-users/2013/Dec/msg00057.html

SmartRecord (This is an ASObjC-based library for a SmartRecord object. AppleScript records have several limitations: you can't get the keys/labels as strings, you can't delete items from a record, and you can't coerce them to text. Unfortunately the scripting bridge ASObjC relies on has a limitation too: it drops entries whose value is missing value. The SmartRecord will return an error if you pass it a record with a value set to missing value (or if one of the labels is an AppleScript keyword). http://lists.apple.com/archives/applescript-users/2013/Dec/msg00113.html

SmartList (This is an ASObjC-based library for a SmartList object, similar to the SmartSet) http://lists.apple.com/archives/applescript-users/2013/Dec/msg00093.html

(1) Quoted from Shane's December 22 mail to the AS list

Chris' gist page is here:

https://gist.github.com/ccstone

It includes:

• REFERENCES FOR LEARNING & USING APPLESCRIPT lists various references to learn and become familiar with AppleScript.
• Edit_Email_in_BBEdit.applescript finds the selected email message with Spotlight and open it in BBEdit/TextWrangler for editing.
• Desktop_Sweeper.applescript creates a dated folder inside ~/Documents/Sweep Desktop/ with newly swept items.