First, it's important to note that the KI is at its core more a system than a concrete opening. Theory in the opening, however, has advanced with such breadth and depth that the KI will still feel like a complex opening that has to be learned in detail compared to some other system-based openings, such as the London System. White has a variety of ways to respond to Black's opening moves, largely because Black doesn't challenge White's control of the center for several moves and thus does nothing forcing. This results in White having much lattitude. In addition to 3.Nc3, White will also often play 3.Nf3 or 3.g3. We'll return to these two moves later in "sidelines" and Fianchetto Variation posts. After 3.Nc3, Black responds with 3...Bg7, again doing nothing to force White's reply. And now we have the KI on the board.
2. The Four Pawns Attack: 1.d4 Nf6 2.c4 g6 3.Nc3 Bg7 4.e4 d6 5.f4 0-0 6.Nf3
This is an ultra-aggressive approach that has largely been de-fanged at the upper echelons, but which is popular at the amateur level. How could it not be?
And note the consequences of Black playing 6...e5 at this point in time, beginning with 7.dxe5. Take a look now, as Black has to constantly be alert to combinations in the middle of the board.... 7...dxe5 8.Qxd8 Rxd8 9.Nd5, and Black has nothing better than to give up the exchange with Nxd5. The Averbakh Variation thus prevents e5 for a time.
So, the "mental structure" is in place for assimilating the KI. To summarize, we'll begin with
(a) the four major variations flowing out of 3.Nc3 d6 4.e4,
(2) Four Pawns,
(3) Sämisch, and
(4) Averbakh, then
(b) the major line of the Fianchetto Variation, followed by
(c) the "sidelines," which I'll divide into
(1) major and
(2) minor sidelines.