The document has a panel (found via the window menu). It is for that document only and has a limited selection of presets on display by default such as three or four gradients and a few tiles etc but luckily this can be extended to include 100s and 100s of additional colors etc. Adobe have supplied a vast number of additional libraries (in ASE format). You can also find many additional libraries on the web and they will be in AI format. The libraries can contain color, groups, patterns and gradients. The sets supplied by Adobe are clearly defined as gradients, colors etc and you get sets of neutrals, earth tones, ancient, baroque etc and they can then be used for particular projects.
This varies from version to version but generally you can find the location in program files (or applications on the mac) and adobe (or adobe Illustrator on the mac) and presets folder and then you will see en_US or en_GB etc and finally the presets section where you can find the libraries in the swatches section (you can also see all the symbols etc)
It should be noted that all the supplied files from Adobe re in ASE format (with the most recent releases) and not AI format and cannot be opened via the application's open etc commands so you cannot change those libraries in anyway.
Go to the bottom of the menu commands and libraries there with the same breakdown of libraries and categories. Select a file and that library will then be opened in the application.
They can be accessed via the panel (found in the window menu). Go to the open command at the bottom of the menu and it will expand out to show all the available libraries and you will see the list include art history, celebration, earth tones, neutral, scientific etc and you will also see an entry for gradients and many of those categories also come with a huge number of different readable (but not editable) ASE files to access such as foliage, brights etc. Just select the entry and the library will be opened. The presets included in the library are not added to the document. You only do that when you actually click on an entry in the library (it does not have to be used)
If the ASE (or AI) files have been added to the presets path then you will be able to see them all super quickly via the bottom of the color libraries (such as foliage). The first item at the bottom is the list of all the accessible libraries such as history, celebrations, corporate etc so you can access the ASE / AI files there. You can also scroll through the libraries in order of their name / category (they are in alphabetical order within their category only) and you will then be able to quickly select a texture or basic graphic lines or animal skins etc to create all kinds of amazing designs.
If the source files for the presets is in AI then they can be opened via the file open command as a standard file. If you then go to the panel you will see all the entries in that file and you can then double click the entry (if a tile etc) and edit the design and then save a copy etc of your changes in the editor. You can then save this document via the file save command and those designs can then be used in other documents.
If the library is not stored in the presets path then you can use the option of other library command found at the bottom of the list of categories and you can then browse for the AI or ASE file in any other folder. Once founded it can be selected and then used within the application in the same way.
If you want the libraries to remain from session to session, go to the library (not the document's panel) and then right side menu and down the bottom and select persistent. Personally, rarely want that but it is an option.
You can save all the current presets to an AI file as well as to an ASE file. The ASE format is the one used throughout all the preset libraries but when saving, you can't save patterns etc with that format so you will have to use the AI format. How to do this, go to the bottom of the panel and the first icon with all the list of libraries, that has an option to export the current presets to a new file (AI format). You can also go to the right side menu of the panel and down at the bottom of the menu you can export for the AI and ASE format. Personally, I will always use AI but if you want ASE you cannot export the gradients etc. When you perform this action, the AI file will be placed in the user section of your PC or mac and you will then see the library appear in the user defined part of the long list of libraries, just above the other library option.