WORKING
Assume one of the transistor, say TR1 become conducting at first. Now, since TR1 is conducting, it's collector emiter voltage should be ideally zero, but any way, it will be around 0.1 volt and it's base emiter voltage is +0.6v. Now the capacitor c1 will start charging. When the base voltage of TR2 become +.6 due to the increase in the c2 voltage, the transistor TR2 starts conducting. At this moment, voltage at TR2 collector becomes low. The low voltage (<.6) is coupled to TR2 base and this makes the TR1 to become non conducting. Now when TR1 become non conducting, the collector voltage of TR1 become high due to the resistor R1 and this is coupled to base of TR2 to make it perfectly conducting state. Thus now TR2 become conducting and TR1 become non conducting. Now since TR2 become conducting, c2 starts to charge and thus the base voltage of TR1 is gradually increasing. Now, when it reaches >0.6v, TR1 becomes conducting and this reduces the voltage across TR1 collector and this low voltage is coupled to base of TR3 via capacitor c1 which makes TR2 nonconducting. Now the high voltage from TR2 collector is coupled to TR1 base via capacitor c2 which makes the TR1 completly conducting. Now the above process repeats and thus the transistor become ON OFF alternatively. Thus it is called as an astable multvibrator.
Now instead of R1 and R4 if we are connecting LEDs , we could observe that the LEDs are toggling alternatively.
Now,
frequency of the astable multivibrator is as follows:
F = 1/[.693(R3.C2 + R2.C1)]