I don't understand why harmonics occur in signals. So if I receive a time domain sinusoidal signal at 10 Hz and I perform the FFT of it, I will observe peaks at 10 Hz, 20 Hz, 30 Hz, and so on... with amplitudes decreasing, but why? Should it just not be one peak at 10 Hz?

For e.g. if I was to synthesize the time domain signal with this frequency graph, would I not then have now a sine wave of 10 Hz, 20 Hz, 30 Hz, etc. added up together when it should just be a sine wave at 10 Hz?

Maybe I haven't worded the question correctly, but hopefully, someone could try understand and lead me to some resources to help get my head around harmonics in general...