I am attaching a screenshot of the analysis I ran of it. But in any case, LTSpice says your circuit works. The LEDs altering on/off cycle whose flash rate is control by the two 22uF capacitors and the two 10K resistors. While today most people use a NE555 timer IC this version is simple to build. Oscillators are tricky circuits, and in my opinion their designers are magicians (especially those YIG oscillator guys). Here is a blast from past as they say with a transistor astable multivibrator. You might also think of the transformer as the feedback path that provides the necessary phase-shifted feedback from the collector (output) back to the base (input). That phase shift is what causes the circuit to oscillate. time signal, but with a phase shift between them. In this circuit I suspect that phase shift is the most important feature of the transformer, allowing the collector and base to see the same voltage vs. But it would couple the two sides of the circuit, while providing a phase shift between them. So you are right, this transformer would not boost voltage. This type of transformer is often called an isolation transformer. But a transformer can have an equal number of windings in the primary and secondary, in which case it does not increase or decrease voltage. Confusion arises because common transformers step voltages up (or down). So while your component isn't "an inductor", it is "two inductors". Of course, a transformer is just two inductors with linked magnetic flux. Also, the dots and dashed lines indicate "transformer". Since this thing has four terminals, it can't be an inductor. First, an inductor is a two-terminal electrical component.
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