Greetings, I've been reading some music theory and have a basic understanding of chord construction but something just isn't right.

Much literature says the major chords are a set of triads and triads have 3 notes. That isn't a problem yet the major chords that I know have more than 3 notes. For e.g. C as a triad is CEG yet as a major chord it is ECGEC (from bottom string up). Why is that?

Note there are only three individual notes, regardless of the fact some notes are repeated. This is what they mean by 3 notes, three different notes.
A basic triad is just: tonic, major or minor third and the dominant 5th. Any repeated notes are just added notes to make a fuller sound. Any notes apart from the triad that are added change the name of the triad and extend it, like a major 7th, a 9th, flatted 5th, etc.
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ECGEC is still a C Major chord, it's just seems weird because of how the guitar is tuned. You'll find that the majority of chords on the guitar are in some kind of inversion because it's pretty much impossible to play them in root position. At least not comfortably anyway.
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