Error screen after formatting my macbook
I formatted my MacBook Air a few days ago in order to decongest it because it showed I had barely any disk space left despite me removing almost everything from the computer. Before formatting it, I backed the hard drive up to an external drive in Mac OS Extended (as recommended on a post). After formatting the laptop, I was taken to a menu which had options such as Restore from time machine backup or reinstall the OS etc. I chose to reinstall the OS since the reason I formatted the paptop was because of the issue with disk space, and restoring from the backup will essentially just take up all the space again. After about 4 hours of the reinstallation process, the installation stopped and the computer froze. I decided to restart the computer. The computer did not automatically go back to that menu, so I pressed Cmd + R as recommended online. This took me back to the menu and at this point I needed my computer to work so I may do assignments. I chose to restore the backup instead. After an almost complete restoration, I got an error message stating that the restore cannot be completed. Baffled, I restarted the computer. When I restarted it, it said "the computer was restarted due to a problem" or something along those lines. Since then, right after displaying that message it will give me an error message which I have attached though a picture. Immediately after showing that code, the computer restarts and does the same. Over and over again. I am a student and do not have access to funds or an apple store, which is why I decided to format it myself instead of seeking professional help. Please help me understand what is going on and how I may fix it. Thank you.
MacBook Air, OS X Mavericks (10.9)