I've marked the main ground which in the schematic is represent by 'Strip line' and the op amp ground which written as V03 ( a bit strange when He use V03 +5V and V03). I've heard about ground loop and notorius things about it. But my question is why do we need to separate the ground reference?. If so, why the voltage adjustment part where there's some voltage divider on it use the main GND and V03 at the same time?.
It really should be called common instead of ground.
There are two "commons", the output negative and the output positive. All of the control circuitry is referenced to the output positive marked Vo3. There is a floating +/-5 volt supply also referenced to Vo3. The advantage of this configuration is that the control circuitry can control a higher voltage than its supply voltage. The disadvantage is the requirement for a floating supply. In this case it allows the 30 volt LM324 operational amplifier to control up to 30 volts, which would otherwise be difficult. Alternative designs could have used a common 40 volt operational amplifier.
The voltage error amplifier is comparing Vo3 at its inverting input to a divided down output, plus an offset generated by the Vo3+5V voltage divider, which becomes the reference.
Hmm, that capacitor across the 100k potentiometer is a mistake because it would add phase lag but it shows no value so was probably left out.
HP/Harrison made a lot of power supplies with this bootstrapped configuration.