YouTube allows you to organize your favorite videos into playlists and share them with other users. The sharing of video playlists on third party websites is facilitated through the use of embed codes that can be inserted directly into the HTML code of the desired webpage.
Find the Embed Code of a YouTube Video Playlist
Click on the YouTube menu > My Channel to go to your homepage. Click on the Playlist tab and select the playlist you want to embed. Now click on the Share button displayed below the video playback screen > Embed:
You can embed the entire playlist or start it with a specific video. Tick the Share with playlist starting from checkbox and then choose between current video and start of playlist:
Click on Show More... to customize settings such as Video size, Show player controls, Show video title and player actions and Privacy-Enhanced mode. Once done, retrieve the embed code and paste it in HTML code of your website.
You can also use a playlist featured on another YouTube channel. Visit the homepage of the desired user (search with the username), navigate to the Playlist tab, and choose the playlist. If the user has turned off video embedding on his channel, then you will have the Embedding disabled by request message displayed instead of the embed code: