MPPT charging a li-ion battery
This IC has an integrated MPPT controller that uses a perturb and observe algorithm so if the IC is not in CV or CC mode is in MPPT mode. The voltage on the output depend on the state of charge of the battery but you can define both a maximum CV charge and a maximum CC charge. For the CV you use R6 and R5 in order to get 1.25V from the voltage divider, that is, CV_set=1.25*((R5+R6)/R6) if you want to start charging with constant voltage at 4V just change the resistors accordingly. For the CC you use R4, the voltage drop shall be higher than 50mV to start CC so CC_set= 0.05/R4, so in the case of your figure the CC will be 50mA (quite low), so if you want to increase it just decrease the value of R4.

You can connect the battery to the output of this IC, you don't need anything else but the voltage is not and cannot be regulated, as I stated before it depends on the state of charge of the battery. It is clamped to the battery voltage. 

I recommend you to install a protection IC for the Li-Ion cell so you can define a secondary protection for both overvoltage and overcurrent, this ICs normally include protection against short circuit and undervoltage too, this is very important otherwise you can keep discharging your battery to dangerous levels.