Simplest possible circuit for charging a li-ion cell
I've been using this for quite a while and it works. I charge pairs of two Li-Ion cells in parallel with it.



Source: Electronics DIY

A major disadvantage is the large heatsink required by LM317. Mine is 10 by 10 cm and still gets quite hot. Instead of R1 - R2 I used single 2.2 ohm / 5 W resistor (that's what I had).