This is one of the highest profile chapters in the bible, and deservedly so. The theological implications span much of the bible, and this is widely considered foreshadowing of the sacrifice of Christ. But I don't want to get ahead of myself quite yet. We still need to establish the proper context.
Remember in the last chapter what happened, and really the entirety of Abraham's life. He was childless for about 86 or 87 years, yet he held the promise from God of not just one offspring, but of the sand on the seashore and the stars in the sky (two separate promises at different times, but reaffirming the same message).
And this brings me to a point I was planning on raising from a later verse, but I'll just say it now; double repetition is a device used in the bible to denote strong, powerful emphasis. This is relevant to the two "main" promises to Abraham. Though admittedly he is given the promise a couple more times in other ways, I consider these the two most prominent, descriptive and specific promises.
We will see double repetition of certain things from now all the way through the NT, where one of Jesus's most repeated phrase is, "Truly, truly." This could also be considered another angle on some of the repeated stories in the bible. For instance, the two accounts of the creation of man in Genesis 1 and 2 could possibly be considered a slightly more elongated double repetition for emphasis. This is all an aside, though.
So Abraham has this promise of a son, and then there's the whole Ishmael drama. After that, miraculously Abraham has another son by Sarah, who God says is the promised son. Last chapter, after more conflict Abraham throws out Ishmael and Hagar, so in terms of children still with him, he is only left with Isaac, the promised son, his joy and his future.
Verse 2: Take your son, your only son, whom you love, Isaac (which means laughter), and go offer him as a burnt offering. You can see repetition, again. This time it is emphasizing "son" and also emphasizing Abraham's love, which is appropriate given the context. This really is Abraham's hope of a future, because it is the promised son.
Strangely (to me), it does not at all describe Abraham's emotional response, or anything that happens between the two of them until early the next morning, Abraham and Isaac (with a few servants) saddle up and head off to Moriah. Commentators tend to emphasize the promptness of Abraham's obedience, that he leaves "early the next morning". I agree that this is a striking response to such a difficult request. However, we are left without any other textual indicators of how Abraham (or for that matter, Isaac) responded to this command. Note that Isaac is not actually told he is going to be sacrificed. He is left questioning Abraham later on the journey, and only at some unspecified point later, he seems to figure out what's going on. So as far as I know, Abraham is the only one aware of the purpose of this journey.
So what we know is that Abraham responded promptly and (understandably) didn't tell Isaac. In verse 7, Isaac asks where the lamb for the sacrifice is. Abraham's response is considered by many to be a prediction of the coming Christ. It can also be considered somewhat implicit foreshadowing of the Passover, though in the Passover the people themselves provide the lambs, so it is really much more directly related to the Christ. What Abraham says is that "God will provide [for] himself the lamb". I put  around "for" because some (obviously Christian) commentators suggest that it is not implied in the original text, that "God will provide himself the lamb", which is of course a much more direct prediction of Christ, the lamb of God.
At this point, there are a few perspectives on what's going on in Abraham's mind. For his last statement, either he is trying to invent something comforting, or he is actually knowingly prophetic. As for the sacrifice, some people say that Abraham is expecting God to raise Isaac from the dead after he is sacrificed. This opinion is somewhat reinforced by a verse in Hebrews, which talks about Isaac's offering. The other, more direct opinion, is that Abraham really thought Isaac would die. But that leaves a paradox, how the son of the promise, the father of nations, would have children though he was dead. That's why he might have to be raised from the dead. But regardless of what Abraham thought, these are the issues he had to face.
About this point, Isaac is either told or figures out that he is the sacrifice. Or Abraham just starts tying him up. More likely the former than the latter. Also interesting to me, Isaac's reaction is not recorded either, and I'm sure his emotional response must be at least as poignant as Abraham's. It's one thing to have to sacrifice your promised son, it's another thing to be the son being sacrificed! I'm slightly, but not overly, surprised by Isaac's obedience. At no point is he described resisting. This is not because I think he is eager for death, but because of the very strong culture of patriarchal obedience in this time. Abraham is the lord over his house and Isaac, even his favored son, must conform to whatever Abraham desires. So that's why I'm not fully surprised, but even so I am mostly surprised at how little of his reaction is depicted.
Just as Abraham is about to stab Isaac, an angel speaks to him, with Abraham, Abraham (2x repetition). Abraham sees a ram, and thus what he spoke before comes true, that the Lord did provide a lamb. And the angels repeats Abraham's two promises regarding his son, the sands of the seashore/stars of the sky. This is another 2x repetition. Abraham leaves and goes to Beersheba, the well of the oath.
Lastly, Abraham discovers that his relatives had a number of children. I don't think this is particularly relevant to the story.
So yeah, in summary, I think a diligent scholar could mine a lot out of this chapter, as indeed many scholars have. I'm not going to go into a lot of that, but anyone who's interesting can do so pretty easily by just Googling it. It is one of the most important events in Abraham's life, and in many ways it defines his faith: his willingness to sacrifice all, simply under the command of the Lord whom he obeys in accordance with the promises given and fealty that he swore.