Can some one explain radio harmonics to me?

Sounds like is came from a lame electronics course handout.

Harmonics are integer multiples of the fundamental frequency.  However, "unwanted" should not be in the definition as harmonics are sometimes desirable.

In audio systems, harmonics are generally discouraged (distortion).

In some audio systems (guitar amplifiers, some hi-fi systems) odd-order harmonics are desirable.

Radio transmitters, harmonics are not wanted at the antenna terminals, but may be desirable in earlier stages.

In digital systems, you want lots of harmonics (square wave).

The fundamental frequency is the desired frequency 

There is usually a filter to filter out the other frequencies 

But the harmonics can still be transmitted

Usually the harmonics are integer multiples 

harmonica create distortian , sound and radio signals are not a pure signal but made up or varies signals . harmonicas are made by this , best is sound signals , ,.05% distortian is better than 1% distortian .

A Harmonic is a third and fourth frequency generated as a result of two primary frequencies.

If you  take an antenna and generate a frequency of 1000hz on it. Then take a second generator and produce a second frequency of 710hz on the antenna, at the same time, it will radiate: 1000hz, 710hz, 1710hz and 290Hz.

This is the sum of the two primaries and the difference of them.

The 1710hz and 290hz  are Harmonics of the two primaries.

If there is nothing but the carrier being transmitted then all you have is the fundamental and nothing else. But when you modulate the carrier with a signal, the very fact that it is then not a constant level/ constant frequency signal means there are other frequencies present. It is just a mathematical fact that any wave other than static level sine wave is made from multiple frequencies. The exact nature of these other frequencies depends on the type of modulation. 

The tool is called a spectrum analyzer and portable, big and heavy. I used it in radar and the largest harmonics are half and twice the carrier frequency. Stagger tuning the klystron is the best way to lower harmonics to insignificance. Harmonics are bad. Radar is radio frequency but called microwave frequency.

harmonics are multiplies of the fundamental. Harmonics of 35 MHz are

70, 105, 140, 175 MHz, etc.

they create distortion in that the resultant of including harmonics is a distorted sine wave, whereas fundamental only is a pure sine wave. reference has some examples.

Basically any periodic waveform, for exam[le a square wave, can be represented as the fundamental plus any number of harmonics added to it. Look up "Fourier series" for more info on this.