Harmonic sine waves typically have less energy than the fundamental. Each harmonic has a frequency at an exact integer multiple of the fundamental. For example, a complex wave may have second, fifth, and sixth harmonics. To get their frequencies, multiply the fundamental's frequency by 2, 5 and 6, respectively.
Odd-numbered harmonics always make mirror-image wave shapes. The positive and negative parts of the wave have symmetry with each other. Triangle and square waves have only odd harmonics.
If the positive and negative parts of a wave don't have symmetry, you can be sure it has even-numbered harmonics. Rectangular pulse and sawtooth waves have mixtures of both even and odd harmonics.