Fourier Series

$x(t) = a_0 + \sum_{n=1}^{\infty}\left[a_n\cos(n\omega_0 t) + b_n\sin(n\omega_0 t)\right]$

A square wave of amplitude $A$ contains only odd harmonics:

$x(t) = \frac{4A}{\pi}\left(\sin\omega_0 t + \frac{1}{3}\sin 3\omega_0 t + \frac{1}{5}\sin 5\omega_0 t + \dots\right)$

This explains why sharp digital edges contain high-frequency energy (and cause EMI), and why distorted mains current contains harmonics.