Apparently, BFE is meant to stand for "Before First Encounter", or before the events of the Serious Sam game. Technically, most of the events of Serious Sam TSE took place before TFE, you know, because all those civilizations came after Ancient Egypt.

I'm not really sure what Serious Sam 2 was meant to be, unless it was meant to show other worlds that Mental had conquered. Given the game's ending, I would have thought that Serious Sam 3 would have picked up from there. Guess not.

:END NITPICKING:
Ok, so Serious Sam 3 is meant to take place in the events leading up to, and when Mental invades Earth, presumably leading to the point where the United Earth Government (or whatever) locates the Timelock, and selects Sam as the one to enter it.

I haven't any more details than that, but I wonder if BFE really does pick up after Serious Sam 2, and Sam decides to pursue Ye Olde Cliche of "My God! He's too powerful to defeat in the present, I must return to the past and give myself and/or the Earth's Leaders all information I've gleaned thus far!".

Or maybe Croteam's strapped for ideas, and they pulled a "Reach"-around. (Ha!)

Best F******* Edition

Also, I think it should be noted that the screencaps currently available are at least circa. 2007. I can swear I've seen at least two of the five in a Russian-language, Ukrainian-published magazine article. In English the title is "Gameplay!". I've lost the issue, and I can't find a link, but maybe someone else still has it?