You can add playlists that you've created, playlists that other creators have made and videos that you've added to Watch Later to your You tab. Saving playlists allows you to easily find and view them later.
If you own a playlist, you can publicly add it to your library so that your viewers can add it to their own libraries. You can update your privacy settings to remove your playlists from view. By removing them, you can still see saved playlists in your channel but other viewers can't.
YouTube app
Add a playlist to your library
From a channel page
- Tap the PLAYLISTS tab to view playlists for that channel.
- Tap More
next to the playlist details.
- Select Save.
While watching a video
If you're watching a video that's part of a playlist, you'll see the playlist name at the bottom of the video player.
- Tap the down arrow
and Save to add the playlist to your library.
- You'll see a tick
when the playlist has been saved to your account.
and 
To remove the playlist, tap the tick 
View playlists that you've saved and created
To view playlists that you've saved and created, go to the You tab.
Mobile site
Add a playlist to your library
While watching a video
If you're watching a video that's part of a playlist, you'll see the playlist name at the bottom of the video player.
- Tap the down arrow and Add
to add the playlist to your library.
To remove the playlist, tap Add 
View playlists that you've added to your library
You can view playlists that you've added to your library and created by tapping the Library tab 