Fonts in Username/LibraryFonts not showing up in applications

There's really only three reasons they wouldn't work, and one of them you can automatically ignore if you've used them on your Mac before.

1) It's not a font OS X supports (the one you can likely ignore)

2) A font (or multiples) are damaged or incomplete (such as not having both parts of a Type 1 PostScript font)

3) You have font conflicts.

Launch Font Book and choose the menu option to Restore Standard Fonts. Besides restoring some fonts (not all) installed by OS X from the hidden recovery partition if you've removed any of them, it also moves all fonts installed by the user out of the System and root Library folders. Each Fonts folder in those two locations will have a new folder next them called Fonts (Removed) and will contain any third party fonts the command moved.

The command does not touch the user account Fonts folder. So if the conflicts are happening because of any fonts in that folder, nothing will change. You will have to manually empty that folder by moving the fonts to a new folder on the desktop. Or anywhere else you want to temporarily move them to. Be sure to do this for the next test.

Now repeat the process of the Safe Mode startup and back. When you launch Font Book, only fonts installed by OS X should be available. Check your apps. If all fonts show as expected, then third party fonts were causing the issue. It's then a matter of figuring out which ones. If you still can't even see all OS X supplied fonts in all apps, then a reinstall of the OS is in order.

Or, as a last test before going through that much time, create a new test user account and login to that. If everything works as expected there, then the issue has something to do with your normal user account. If the issue is the same, then it's definitely the OS.

Restart the Mac into Safe Mode by restarting and holding the Shift key. When it gets to the desktop, restart normally.

Among other things a Safe Mode startup does, it clears out Font Book's database, which a corrupt one is usually the reason for this problem. When you get back to the normal boot desktop and launch Font Book, it will build a new database.

Try it again, only this time when you boot back normally, don't relaunch Font Book. That will take its database out of the equation. Then the OS will consider any font in the three main Fonts folders (System, Library, user account) as active and they all should appear in all apps.

If they don't, then you likely need to reinstall the OS.