This circuit provides a fairly high voltage gain of 40 (32dB) using two common emitter stages, the main design challenge of this circuit is making sure one stage does not excessively load the previous stage or source, the input 10k resistor simulates a source of moderate impedance, a Darlington pair configuration provides a low impedance output ideal for driving a power amplifier, this circuit does not use every trick in the book base bootstrapping and global feedback can improve input impedance and gain.
As a simple rule you should avoid single stage gains above 10 to prevent nonlinearity.
