Mac air, shutting down

Reinstall El Capitan Without Erasing Drive

Please be sure you back up.

1. Restart the computer. Immediately after the chime hold down the Command and R keys until the Utility Menu appears.
2. Select Disk Utility and click on the Continue button.
3. Select the indented (usually, Macintosh HD) volume entry from the the side list.
4. Click on the First Aid icon in the toolbar. Wait until the Done button activates, then click on it.
5. Quit Disk Utility and return to the Utility Menu.
6. Select Reinstall OS X and click on the Continue button.

Also, see this User Tip: Basic Steps for Upgrading OS X.

You well may have a drive or SSD that is failing or has become corrupted. Can you boot from the Recovery HD? If you can, then you can see about repairing the drive/SSD. If you are not able to startup still, then try an Erase and Install.

Install Mavericks Through El Capitan from Scratch

Backup if possible before continuing.

1. Restart the computer. Immediately after the chime hold down the Command and Rkeys until the Apple logo appears. When the Utility Menu appears:
2. Select Disk Utility from the Utility Menu and click on Continue button.
3. When Disk Utility loads select the volume (indented entry, usually Macintosh HD) from the Device list.
4. Click on the Erase icon in Disk Utility's main window. A panel will drop down.
5. Set the Format type to Mac OS Extended (Journaled.)
6. Click on the Apply button, then wait for the Done button to activate and click on it.
7. Quit Disk Utility and return to the Utility Menu.
8. Select Reinstall OS X and click on the Continue button.