Mkay.
A chord is, essentially, two or more notes being played at the same time. The most prevalent form of a chord is called a triad, ie, a chord made up of three distinct notes. Of the triads, there are four main kinds: major, minor, augmented and diminished.
Major triads are made up by a root, a note a major third above the root and a note a perfect fifth above the root. Minor triads are a root, a minor third and a fifth. Augmented triads are a root, a major third, and an augmented fifth. Lastly, diminished triads are a root, a minor third above the root, and then a minor third above that (the name of which I don't think has a name?).
Using those four chords, triads can be made using every note in a key and only the notes in a key. However, one cannot just use one type of triad, to remain in key except in very special cases. For example, in G Minor, the allowed notes are G, A, Bb, C, D, Eb, F. If these are used as roots, than the chords must be, respectively: Gm, Ad, BbM, Cm, Dm, EbM, FM.
In addition to having 7 triads that lie within a scale, each triad has 6 inversions, as to make a palette of 42 triads. An inversion, basically, is changing which notes are highest in order to make the chord sound slightly different. Eg with FM, the basic ordering is FAC. However, there are also 5 other possible orderings, being: FCA, AFC, ACF, CFA, CAF. Using another one of these retains the same basic quality of the chord, but makes it sound slightly different (in that thingy I sent you, I used a chord inversion of the final chord to differentiate from the technically same chord that ended the previous set of chords).
I don't know much about chords that contain less than or more than three notes. However, I just assume that notes a further third above the highest note keep being added (a seventh?). We also know, that i(n) = n!, where i is the number of possible inversions, and n is the number of notes in a chord. This allows xTreme small variations depending on how complex you want your chords to be. But I also assume that the more notes you add to a chord, the more similar they sound, as there can be less actual variation, as they converge on containing all the notes. Hence triads as being the preferred kind.
I also don't know much about what makes a sequence/progression of chords good, other than the just "play it by ear" method. Is there more?
Lastly (alsoalso doesn't grammar right here) I've seen little numbers used to denote the chords, but I'm not sure what they refer to.
So that's it?
I'm probably missing some really important large hunk of knowledge.