My MacBook Air keeps restarting
Do you have a Time Machine backup on an external (USB, FireWire) hard drive? If so, boot to Recovery (Apple + R), erase the drive and reinstall OS X, then restore your data via Migration Assistant. 

Your core issue here is you do not have enough space on your hard drive for all your data. You're going to have to either:
 - Delete some of your data or
 - Clone the old hard drive to a larger drive (this is the perfect time to upgrade to a SSD, also).