I have a laptop which was previously a windows one(NTFS). I reformatted the drive to a half FAT32 and ext3 to dual-boot. A week later, my mother tells me about some important Outlook emails I erased. Is it possible to recover these files, after the disk was reformatted? I'm certain that the file was on the FAT part, near the beginning of the drive. How would I get the emails back?

Fat part, beginning of the drive? You go pay someone a lot of money to do a hard drive recovery, because you've probably overwritten the files way to many times just by installing a new os.

Most likely, you don't get them back. The free tools that are online aren't going to help after you've installed a different os on top of the original files.

As Caeda said, if you've overwritten the files, they're pretty much done for. At this point, you're talking about electron-microscope level recovery to get at residual data on the side of the track. And even that would be iffy.

Yes I agree, if you already have reinstalled windows, chances are that you have overwritten the files. If not you could try the tools avalable. I have had some success with Filescanvenger in the past, but I think that works on NTFS partitions. Actually I recently formatted a parttion by accident to FAT32. I reformatted back to NTFS and recovered most of my files (this wasn't an important partition, so I left it completely idle until I had rocovered the files).
You will need the name of the outlook .PST file in question, but don't get your hopes too high. The chances are slim.