The theory is simple:another thing...is the theory of operation of this circuit the same as its application?
1) The output of the 555 goes high and slowly charges the output capacitor through its output resistor.
2) The transistors have their inputs connected in series so when the rising capacitor voltage reaches +0.7V then the first transistor turns on. When the voltage reaches +1.4V then the second transistor turns on.
3) What happens when the voltage reaches +2.1V?
4) When the 555 times out and its output goes low then the diode at its output quickly discharges the output capacitor which turns off the transistors so they are ready to begin again.