Hello, I would like to know one thing to increase the gain of a wave trace what should I use a “amplifies” or “compressor”, and what a difference. Thank you

“Amplifier” is used to increase the amplitude of all of the selected section of the waveform: making all of the sound louder in that section.
“Compressor” is used to reduce the difference in volume between the loud and quiet sounds by reducing the gain when the waveform exceeds a threshold: quietening the loud sections.

And the third tool that does a similar job is “Normalize.” Normalize lets you pick the volume of the loudest part of the show and it adjusts both left and right differently until that loudness is achieved. The tool is different between Audacity 1.2 and 1.3. 1.3 lets you choose the target loudness.