Yes, you can listen to songs stored locally on your hard drive with the Music app, which is located on your desktop. Click on the icon once to open it. When the Music app loads, you will see some songs that already come with your computer. You can add as many songs as you like from your own collection, or by downloading more from the internet.
To add the music to the Music app, first make sure that you have already copied your songs to a folder on your computer, or that you have a device plugged in (like a USB or external hard drive), that has the songs on it . Then, just click on the settings icon in the Music app which is at the top right-hand corner, and then select the “Add Music” button. Select the folder where you have your songs, and upload them to the Music app.
If you have an internet connection, you can also stream music from radio stations on the internet, YouTube, or use web apps like Spotify that come preloaded on Endless.
Starting from version 3.0, Endless OS will include the ability to purchase and install a new codec to support more audio formats. Please see here for more details.