The first section of the 555 timer is wires as an astable oscillator with R2 and C1 setting the frequency. The output is available at pin 5. The second section is wired as a phase inverter. That output is available at pin 9. Resistor R3 and R4 keep output transistor Q1 and Q2 from loading down the oscillator.
The two transistors drive the transformer push-pull fashion. When one transistor is biased-on, the other is cut-off. The transformer is a 120V/18V center tapped that is connected backwards, so that is steps the voltage up rather than down. Oscillator circuit U1, R1, R2 and C1 operates from about 4 to 6V with very stable output.
