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In fourier series we are actually using a different representation of the signal in terms of the sum of harmonically related sinusoids which is very important in signal and system analysis

but in fourier transform, we use it mostly for aperiodic signals right?

but what exactly does this function represent?

[tex] X(j\omega)= \int_{-\infty}^{+\infty} x(t) e^{-j \omega t} dt[/tex]

we have a function in the frequency domain, so in the x axis we will have values for [tex]\omega[/tex] while on the y axis this function, which represents what exactly? and why is it so important?

can you please explain in the most simple words? thanks :)