There is many ways to charge batteries, but Lithium based should take with with special attention on temperature, current and charging time.
My advice is to use dedicated IC for this purpose. I use many times MCP73832 to charge phone size batteries and 18650. This IC support up to max 500mA of charging current, also there is ICs which support even 1A of charging current.
This IC require very small PCB area, circuit is very simple and require small number of parts :
On other side of that PCB I made Li-Po/Li-Ion to 5V StepUp to power device with 5V from 3,7V battery :
hello peter. Thank you for your full reply and schematics. you are a smd maniac.. he he...
Unfortunately the ic Costs around $10 while a charger costs $5 :/ I will not build that project in the end.
Probably will buy that charger he he to charge my bicycle's torch.