You've studied triads, seventh chords.  But what of beyond seventh chords?  That territory is of 9th, 11th and 13th chords.  These are called extensions, as they go beyond an octave within a chord.  Beyond an octave you have the following:

9th (equivalent of a 2nd)
10th (equivalent of a 3rd)
11th (equivalent of a 4th)
12th (equivalent of a 5th)
13th (equivalent of a 6th)

In a triad you have already two of those, the 10th = the 3rd, the 12th = the 5th.  So the use of these isn't an extension.  But adding the remaining three do result in extension chords. 

Remember the following:

1. Extended chords are named by the largest unalterd interval in the chord.
2. Extensions do not change the chord's harmonic function.  A dominant V chord will still be a dominant V chord.
3. Extended chords have the same quality as the seventh chord that they are built on.  (minor seventh chord + 9th = minor 9th chord)

Ninth Chords

Ninth chords are created by adding a major ninth to an existing seventh chord, whatever quality it has. 

Eleventh Chords

Eleventh chords are created by adding a perfect eleventh interval to an existing ninth chord.  There are some exceptions.

If you have a major 9th chord or a dominant chord, and you add a perfect 11th, you will create a very dissonant chord.  To decrease the dissonance raise the 11th by a half-step.  You reflect this alteration in the chord name like so. 

If you have a minor ninth or a flatted 5th chord, then the perfect 11th is not dissonant against the minor third.  So you can leave it alone.

Here are some rules to show you how it works:

1. Chords with a major third, use a #11
2. Chords with a minor third, use perfect 11th

Now if you have an 11th added without a 9th, then you actually have a "suspended chord."

Thirteenth Chords

Thirteenth chords that are "complete" are built by adding a major thirteenth to an existing eleventh chord.  You should note that extended chords won't always have ALL of the notes that it theoretically should have.  In a thirteenth chord it is popular to leave out the eleventh.  If the eleventh is in the chord and it is altered you must show that is.