Doing Non-Destructive Installations?

I tried to install TDE-Kubuntu Precise (http://ftp.fau.de/trinity/cdimages/kubuntu/precise/) and was told there is another version of linux there.

I was then offered a choice to 'install alongside' (I don't have enough space) or to 'replace current linux'.

I chose 'replace current linux' but was told this would use the entire disk and all of my personal files would be erased! I want to install the new OS, I don't want to format the entire drive and lose all of my files.

Is there a way to install linux without losing 700MB of my personal files?