The fundamental is the frequency that corresponds to the note you are hearing. Harmonics include the fundamental; it is called the first harmonic. Harmonics 2 and above are frequencies of other, faster modes of vibration of the instrument. They are calculated by multiplying the frequency of the fundamental by 2, 3, 4, and so on. These vibrations are one of the big factors that make one instrument sound different than another and are what you are most often altering when using an equalizer.

Fundamental frequency and harmonics can also be applied to anything which is measured in hertz. (hz) For example, in the application of acoustics in a room that has paralell or near paralell surfaces you will get standing waves. The fundamental is a frequency where the wavelength equals tha distance between the two surfaces. If, for example the fundamental were to be 50hz, then harmonics of this frequency would be 100, 200, 400, 800, and so on. This has to do with something you learned in high scool physics. Did you ever do the experiment using a long spring to show that when it vibrates it does so in equal divisions of it's length? The same applies to a guitar string. The 5th string on a guitar is tuned to A 440hz. When you fret a harmonic at the twelfth fret you get one octave higher, the second harmonic. A 880hz. As you contunue to divide the string in half, you consequently halve the wavelenth each time, raising one octave and doubling the frequency. The same concept is applied to all physics where you can measure using frequency. ie light, sound, etc.
Also there is the idea of even ordered and odd ordered harmonics. Even ordered would be divisible by the fundamental, wheras odd ones would not. Even would be third octave fifth octave etc. You may hear about this in discussions about analog vs. digital. Tube amplifiers are known to create even ordered harmonics on a given signal, where solid state(switchmode-class a, ab etc) and class d(digital)amps create odd ordered harmonics. Even ordered is more musical.

So, the fundamental is the lowest root of a given frequency, harmonics are frequency multiples of the fundamental, and can be divided into even and odd ordered.

Hope this helps.

To add to all of the above: The fundamental is usually the loudest frequency in a sound. The various harmonics of the sound appear at a much softer level. The loudest harmonics usually being the ones closest in frequency to the fundamental. All the harmonics added together (at their various levels) is what gives a sound it's character.

As an experiment, pass a single sustained sound through a very narrow band-pass filter with a high Q (a true parametric eq) while sweeping through the audible frequency spectrum. You should be able to isolate and hear the various harmonics (at least the louder ones).

thanks guys for the reply but your replies and all were just to physics oriented ( since i failed physics in the 9th grade) i mean of course its all physics and stuff but i was looking for an answer which would i could easily apply to mixing u know like what r the fundamental and harmonic frequencies of the guitar the piano the bass the snare the kick the toms etc etc u know something that i could probably look into incase two different instrument sound muddy because their frequency range is almost the same for example the bass guitar and the kick drum or the floor tom like more or less the rule of the thumb type of a thing though thats not possible in mixing

Use your ears ...... don't look for simple solutions you can apply across the board, there's no such thing. Each instance is unique to itself and you should be flexible in your response. This is where the talent and art come into play. Becoming a good mixing engineer takes more that simply learnig a few hard fast rules that you can use in every case. You need to be creative and inventive.

yeah i suppose u r right its all about the ears

Maybe an Audio Spectrum Analyzer (RTA) will help you. Phonics makes one (Dual 30 Band 1/3 Octave Digital GEQ with RTA) for around $250. I bet there are others out there too.

I prefer the stand-alone hardware types over the software versions.

Here's the link to Phonic's site: http://phonic.com/product/product.htm