Here is a simple li-ion charging from the site circuitsdiy.com it does not contain specialized circuits charging and assembled on a regular LM258N. The scheme can be used for efficient charging one cell Li-ion batteries such as in a mobile phone.
Charging through a very common mini-USB connector.
Status shows charging indication LEDs.
A simple scheme which basis are an operational amplifier.
Charges even fully discharged battery.
The maximum charging current 500mA (limited USB power), depending on the battery.
Video of work.