Macbook Air login screen twice
yes its really easy to reinstall it without damaging anything! however a backup is ALWAYS recommended, if you bought it over the Mac Appstore you can just redownload it for free and install it again! or if your computer came with mountain lion you can

Choose Apple menu > Restart, and then hold down the Command (⌘) and R keys while the computer restarts.
If you’re not connected to the Internet, choose a network from the Wi-Fi menu in the right corner of the menu bar (in the top-right corner of the screen).
Select Reinstall Mac OS X, and then click Continue.
Follow the onscreen instructions. In the pane where you select a disk, select your current Mac OS X disk (in most cases, it is the only one available).
To start the installation, click Install.