I inherited a 770 with a 128 mb card. There appears to be nothing on the card but when viewed through a reader on my laptop it reveals a 57 mb swap file.

Is there any reason I should not delete this?

The 770 has a means of adding virtual memory via a swap file on the card and it hides it from the file browser on the tablet. If you delete it, I suspect that the 770 will handle this gracefully and just disable virtual memory. It might not though. If you want to safely delete it (or even resize it to give you a bit more space for your files), you can go into your virtual memory tab of the memory app in the control panel and pick a better size for you.

Having said that, I would recommend keeping that swap file as it will make your browsing experience much better as the 770 is known to run out of memory on more complex pages and the virtual memory gives it some elbow room. Either way, go into that dialog and make some changes to confirm that it is indeed using that file as some people set up swap files manually before the functionality was included in the desktop UI and that could be some orphaned file squatting on your valuable space.

Either way, go into that dialog and make some changes to confirm that it is indeed using that file as some people set up swap files manually before the functionality was included in the desktop UI and that could be some orphaned file squatting on your valuable space

How do I 'go into that dialog'?

Also, would I benefit myself if I put some 'swap file' space on each of my 2gb cards? If so, how?

Just figured out the first part of my question and checked that the swap file is indeed set up as additional virtual memory.

However, on the second part of my question...... should I do this for all my cards (particularly the larger ones) to assure best operation no matter which card I happen to have in?

When you swap out cards, the first thing the 770 does when you open the card door is to unmount the swap space before unmounting the card. When a card is inserted, the 770 mounts the card and then mounts any swap space found. I doubt the setting in the control panel will cause it to recreate a big swap file on the new card but rather it will reflect what it found on the card and make changes when you change the setting. Worth verifying though.

Once you verify what is going on, you can set up whatever scheme you like. I would just keep one card (the biggest one) as the main card you have in your system all the time for normal use and have the swap file on that and keep the other cards for backups/sneakernet/media files.

I did it on my 770 and I have never had any problems with it.

Actually, I tell a lie: You have to be careful no to eject the card too quickly after opening the door, or the system doesn't have the time to umount the swap file. Depending on your luck, many things might or might not happen afterwards ("nothing" being the best and "spontaneous reboot" the worst, sofar).

Anyway, the procedure is quite simple and intuitive: Just insert every card you want to install a swap file on and go through the steps of actually installing a swap file (control panel, etc...). Of course, this means you'll lose a maximum of 64 MB (I never tried my luck by installing differently sized swap files on different cards) on every one of your storage cards.