From the diagram, the blue section is a differential amplifier. The base current of the inputs is not really zero, giving the 741 an input impedance of about 2 MΩ.
The sections in red are current mirrors. The input amplifier drives a current mirror load. The top left current mirror allows large common-mode voltages on the inputs without exceeding the active range of any transistor in the circuit. The top right current mirror provides a constant current load for the output circuitry, regardless of the output voltage . The lower current mirror has a very low collector current, because of the 5 kΩ resistor. It is used as a high-impedance connection to the negative power supply, to provide a reference without loading the input circuitry.
The offset null pins are used to remove any offset voltage that would exist at the output of the op-amp when zero signal is applied to the inputs.
The high voltage gain stage is NPN.
The green section is a voltage level shifter. It provides a constant voltage drop between the top and the bottom regardless of supply voltage. If the base current to the transistor is zero, and the voltage between base and emitter (and across the 7.5 kΩ resistor) is 0.625 V (a typical value for a BJT), then the current flowing through the 4.5 kΩ resistor will be the same, and will produce a voltage of 0.375 V. This keeps the voltage across the transistor, and the two resistors at 0.625 + 0.375 = 1 V. This serves as a bias for the two output transistors, to prevent crossover distortion. In some amps this function is achieved with diodes.
The capacitor is used as part of a low pass filter (on the base of an emitter follower) to reduce the frequency response of the amp to prevent oscillations. This technique is called Miller Compensation and functions as an internal capacitive feedback.
The output in cyan is a push-pull emitter follower amplifier. It is driven by a PNP emitter-follower. The output range of the amplifier is about 1 volt less than the supply voltage, since the collector-emitter voltage of the output transistors can never go completely to zero. The resistors in the output mean that the current provided by the output is limited (about 25 mA for the 741), and the output resistance is not zero without feedback. With negative feedback it approaches zero. The output stage has current limiting circuitry.
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