Muggles' Guide to Harry Potter/Books/Deathly Hallows/Analysis

Overall.
A major point in the final book is the completion of the greater picture, which Rowling finesses better than anyone speculated. The major issues are the dual-core phoenix wands, the Elder Wand, the soul tie or mind connection, the shared blood, and Voldemort's demise and Harry's survival in light of the prophecy about them both. Each aspect has a clue in the past history of the series, which plays into the larger picture of the completion of the full plot at the end:
When all is done, Harry is good to the end, for many reasons. His selfless choice to face Voldemort without fighting back ensures the same charm of love his mother gave him, is now given to all of his comrades defending Hogwarts. (As Harry points out, this is probably why the attacks of Voldemort and the Death Eaters won't stick when they come back to Hogwarts with Harry's body.) He chooses not to reunite the Hallows and makes decisions that will hopefully remove their power, except for the cloak. He chooses to come back to the pain in his body and life, rather than take the easy path to join his family in peace, in order to complete the defeat of Voldemort. However, he also chooses to accept and trust the help and vested interests of others, so it is possible that Harry makes the final leap of maturity needed to make a difference... he puts aside his need to be linked to his family of the past (which he could have chosen) in order to bring hope (rather than despair) to his present "family of friends." This final thought is supported by the epilogue of the final chapter that indicates that his godson Teddy, son of Lupin and Tonks, may marry into the family of the friends who have become family comprised of Harry and Ginny, Bill and Fleur, and Ron and Hermione, who are now all related by marriage.
Possible Points of Confusion.
Why did Harry not die?
We should take a moment here to discuss the complexities of the interrelationship between Voldemort and Harry in the last few chapters of the book. It is not immediately clear why Voldemort does not kill Harry, or why Harry does not die when Voldemort does, there being a blood link there.
First, we should look at the wands. While an interrelation between Voldemort's wand and Harry's has been established, and it is mentioned that the events in the cemetery have made Harry's wand proof against anything Voldemort can throw against him, this is discounted by Christmas. At that point, a charm Hermione uses ends up breaking Harry's wand, and it no longer plays a part in the events. Voldemort, not knowing this, abandons his own wand in favour of the Elder Wand of legend. The Elder Wand will not harm Harry because it accepts Harry as its master – contrary to the apparent path through history, it is not murder that defeats the bearer of the wand, but forcible removal of the wand, so the wand became Draco Malfoy's when Malfoy disarmed Dumbledore, and Malfoy was in turn deprived of his own wand by Harry. Harry is careful to check this with Ollivander in Shell Cottage; this is the point where he begins to understand about the Hallows, and starts choosing his own fate accordingly. (It was Malfoy's wand Harry was holding when he defeated Voldemort. Presumably the Elder Wand recognizes the wand that stood against it, possibly in addition to the bearer.) At the same time, Harry cannot be killed by Voldemort because of the blood linkage – as he is using Harry's blood, he provides that protection. Granted, this may seem far-fetched, as Voldemort certainly had Riddle blood in him, but he had murdered Tom Sr. and suffered no ill effects. Then again, Tom Sr. didn't care about Tom Jr., and possibly didn't even know he existed. As what activates the protection, is being willing to die for someone rather than allowing them to be killed, and neither Tom Sr. nor Tom Jr. would die for the other, there was no protection there.
When Harry approaches Voldemort at the end of the book, then, Voldemort's curse knocks Harry's soul into the waystation, but it is then his option whether to go on or return. If he goes on, taking Voldemort with him, there will still be one Horcrux in Nagini to allow Voldemort to return. However, as the Elder Wand won't harm Harry, he has the option to return, and he chooses that option. As Dumbledore says that the soul fragment within Harry is now gone, the only Horcrux left is Nagini. Once Nagini is dead, thanks to Neville, there is nothing holding Voldemort's soul to the earth.
There is still the blood link, but that is unidirectional: Lily did not die to save Voldemort, did she? So every time that Voldemort uses the Killing Curse against Harry, it will rebound upon him. The first time it rebounded, when Harry was one, it killed Voldemort, but his soul, still held to the earth by five Horcruxes and the soul shard adhering to Harry, remained in Albania. The second time, it partially rebounded, killing the soul fragment in Harry, but Voldemort returned in the same body because he came back with Harry, as he had gone to "King's Cross" with Harry. The third time, with no Horcruxes left, it killed Voldemort outright.
There is, of course, an alternate explanation. Xeno Lovegood had said earlier that the three "Hallows, if united, will make the possessor the Master of Death". We believe that he is quoting the legend when he says this because his speech cadence seems to be written differently than his usual speech. Harry has, at this point, effectively united the three Hallows: the Elder Wand has transferred its allegiance to Harry, the holder of the wand which disarmed Dumbledore; the Invisibility Cloak is under his shirt; and he has been using the Resurrection Stone to navigate through the Forbidden Forest. It is possible that, having become the Master of Death by having united and possessed all three Hallows, Harry will now be the Master of Death until he decides to pass on. It is unknown whether loss of any of the Hallows to another would end his mastery; but it is certain at this point that Harry has become, perhaps unknowingly, the Master of Death, and so may have been able to make the choice himself whether to go on, or return to the land of the living. This also might explain why Dumbledore was in the Waystation waiting for Harry; we know that he had the Elder Wand and the Resurrection Stone in his possession in "Harry Potter and the Half-Blood Prince", and Harry's bringing the Cloak into Dumbledore's office might well have been enough to give Dumbledore also the necessary power over Death to allow him to await Harry's arrival.
What is the nature of the bond between Harry and Petunia Dursley?
We know that Petunia does not like Harry, and Harry absolutely loathes living at Privet Drive. Yet there must be something that keeps them together. At the beginning of "Harry Potter and the Order of the Phoenix", Vernon Dursley, discovering that Harry is becoming a magnet for trouble that can hurt his family as well as Harry, orders Harry out of his house. Petunia seems to agree with Vernon's decision, until the Howler reminds her of Dumbledore's earlier letter, which we must presume was the one left on the Dursley doorstep with Harry at the beginning of the series. At that point, Petunia abruptly rationalizes Harry remaining with them, forcing Vernon to back down. Obviously there is a blood relationship between them, as Lily Potter was Petunia's sister. Petunia, however, throughout the series, acts as though Harry has been thrust upon them; she has not accepted this burden willingly. What is compelling her to keep Harry? And why is Harry required to return to Privet Drive every summer? Granted, it does not have to be for the whole summer – at the beginning of "Harry Potter and the Half-Blood Prince", for instance, Dumbledore, who obviously is privy to the details of the spells involved, collects Harry from Privet Drive after only a fortnight. What exactly is the nature of the bond that requires Harry to stay with Petunia?
It is stated over and over that Harry's protection came from Lily's sacrifice, and that until he reaches 17 that protection will come from her blood – and Petunia being Lily's sister, a blood relative, means that Lily's blood is in Petunia as well. That protection, which is only protection from Voldemort's direct action, as it was Voldemort's direct action that Lily died trying to prevent, ends when Harry reaches the age of majority and is unable under Wizarding tradition to claim Petunia's home as his own. In the first chapter of "Harry Potter and the Philosopher's Stone", Dumbledore says he has reinforced that ancient magic, but it seems that it is that tie of blood relation which counts.
The word "blood" is used in particular so that we can see the transfer of the source of immunity from Petunia to Voldemort himself in the cemetery in "Harry Potter and the Goblet of Fire".
As it was Lily's sacrifice that saved Harry's life, it is the shelter under Lily's blood (by way of Petunia) that keeps Harry protected for the first seventeen years of his life. However, this does not provide any protection to Petunia, as Lily certainly did not die to save Petunia's life. While there is no way that this can be anything except speculation, it is possible that what Dumbledore was achieving with his "reinforcements" was extending Harry's protection so that it protected his home as well as himself. This would explain why the Order were taking the Dursleys away at the beginning of "Harry Potter and the Deathly Hallows". With Harry reaching his majority and no longer able to (even grudgingly) call Privet Drive "home", his protection there was ending, and the protection afforded the rest of the family by Dumbledore's reinforcements was likewise ending.
The suggestion has been made that Petunia herself might have had some input into this magical bond. After all, her sister Lily, as we have seen, was a very powerful witch. At an age where most witches are able to produce only undisciplined magic, Lily, without a wand, was able to control the magic she was able to do, causing a flower to open and close on command. This ability seems to be uncommon in the Wizarding world; Harry's magic was largely out of his control, and of the other wizards we have seen, Tom Riddle, alone of those under school age, seemed to be able to control the magic he could do. Is it possible that Petunia had some magical ability as well, that was tapped to protect Harry? In fact, no; the author has said that Petunia was doomed to be a Muggle for all of her life. While the author had said at one point that some character would do magic late in life, and there was speculation that this would be either Petunia or Dudley, in an interview following the publication of "Harry Potter and the Deathly Hallows" the author stated that the plot had shifted since that time, and the character who had been intended to be a late-blooming witch or wizard had not required that ability. It is possible that Dudley has some trace of magical ability, as he was able to sense the Dementors in "Harry Potter and the Order of the Phoenix", but he never seemed to be able to perform magic. Even if he had had magical abilities, he was largely out of the secret of Harry's background, and would not have been able to help consciously in any event, being underage.