Difficulty with the Beta Lactams!

Can anybody help me understand/remember the Beta lactam classes of antibiotics and their mechanism of action?

I'm trying to learn how the different generations of cephalosporins relate to penicillins and carbapenems, but I'm getting very confused!

It doesn't help that every single one begins with cef so I can't remember which generation is which! Is there any trick to this? Or is it just a case of remembering the names.

Apologies if this is more appropriate for the antibiotics sub but I'm a doing a microbiology MSc so thought I'd start here. I also apologise for the ceph/cef discrepancy; I'm in the UK!