Only the AC component. a transformer won't amplify per say, it will convert from voltage to current or vise versa. Typically used to isolate amplifier stages.
Although you can get voltage or power gain from a transformer, you can't get both at the same time, an increase in one means an inverse decrease in the other. You can't get power gain with a transformer, power in equals power out.
With one transformer you cannot amplify a signal.
However with two transformers a saturable reactor or magnetic amplifier can be made.
Forty or so years ago saturable reactors and magnetic amplifiers were a viable approach. Saturable reactors and magnetic amplifiers are usually not as good an approach as solid state electronics are now.
The older editions of Reference Data for Radio Engineers have a section on Magnetic amplifiers.
I have made saturable reactors using Signal brand transformers. They worked well, but were large, heavy and expensive compared to a solid state amplifier.