Li-ion batteries are essentially large hunks of metal; they cannot be soldered easily..  Even if they could, it's actually quite bad for the cells to absorb that much heat. It degrades their lifespan.  So we need a tool that can deliver an instantaneous powerful spark to connect some nickel strips - and thus the other cells - to eachother to form a battery pack. That is, we need a spot welder!

It is also a good idea to use some top insulating paper for the positive terminals, and plastc frames around the cells.  I 3D printed my own, since I had some (very uncommon) AA-sized Li-Ion cells:

Now there are spot welders on the market of course.  Even ones for hobbyists doing the kind of recycling work described in this project.

The problem is, these "portable spot welders" usually die after the first few months, because the battery capacity isn't large enough to keep on delivering those massive surge currents for welding.  

I bought one, but it died after less than six months.  And it never worked that will begin with:

It looks like such an ideal starter kit! but I was left very disappointed.
It's time for a better solution ---