This resembles two common problems.
If it restarted soon after you told it to install alongside:
Then you are probably using bad installation media. There are two causes:
- Corrupted ISO image.
- Bad write to the USB flash drive (or, if you had been using a CD/DVD, bad burn).
First, check the MD5SUM on the ISO image to see if it's corrupted. If it is, download it again (and test that, too).
If it's not corrupted, boot from the USB flash drive, press a key when you see the keyboard and person icon appear at the bottom of the screen, and select Check disc for defects. (See also this video.) This applies equally for CD/DVD and USB media. That should reveal if the write is bad.
If it is bad, write it again (and test it again). If it's still bad, make sure you're writing it correctly. If you are, and it's still not working, try writing it with a different technique. If you're creating the live USB in Windows, there are two common techniques, so you can try whichever one you're not currently using:
If the installation went on for a while and then it restarted:
In this case, it's still worth checking the installation media, but it's more likely Ubuntu did install successfully, but that the GRUB2 boot loader was not properly installed to the Master Boot Record. To fix that problem, use any of the methods listed in:
If neither works:
Then more information is needed. Please boot from the USB flash drive, open a Terminal (Ctrl+Alt+T), and run:
sudo parted -l
Then edit your question (or, for readers other than the creator of this question, make a new question) to include the complete and exact text from the Terminal (you can copy it to the clipboard in the live USB system, access Ask Ubuntu, and paste it in, then format it with the
<$> tool in the Ask Ubuntu editing toolbar).