Casting spells is a strong theme in all of the books, especially in this one. Books on spells are read (160, 390, 501). Spells are practiced throughout the book, and the students practice and are tested on them (710-717). Spells are used against the villains in a big battle at the end (787-792, 796ff) in a scene I like to think of as the Battle of the Dueling Wands. There is hexing (400), jinxing (354), magical curses (515), and psychic dreams (462-63) which are later explained as Harry's mind being invaded by Voldemort. "Ancient spells and charms" supposedly protect Hogwarts (531). The Pensieve (a container for thoughts) is engraved with "runes and symbols" (529). In actual sorcery, runes are often carved or engraved on occult tools for the purpose of magically empowering them.
Harry secretly teaches a class on Defense Against the Dark Arts for some students (393-395 and elsewhere). Harry does not always use his wand responsibly – he uses it to scare Dudley (13), to threaten his uncle (28), when he's mad at Seamus (218); and several students using magic taught to them by Harry attack Malfoy and his two cronies, turning them into slug like creatures, and hang them from a luggage rack where they are left to ooze (864).
Harry teaches the students of his class how to conjure a Patronus (606-607), entities conjured up for protection. Harry learned in the third book how to do this, and my article, "Harry Potter: A Journey to Power" explains the occult connection to this on page 2 of the online article.
To prevent Voldemort from invading and using Harry's mind, Harry takes occlumency lessons from Prof. Snape (519ff). The idea and techniques behind this are somewhat reminiscent of the psychic technique of visualizing a white light for protection, and of the Zen technique of emptying the mind. I once practiced both of those techniques. Many in the Occult and in the New Age believe that there are people who can psychically drain you or attach themselves to you, and certain techniques are taught to avoid this. Occlumency seems to be derived from, or at the least recalls, these ideas.
What protected Harry from Voldemort? Dumbledore explains that when Harry's mother died for him, her death acted as a protective charm that saved him (835). By placing Harry in his mother's sister's home, Harry was protected further by his mother's blood (flowing in the veins of her sister, Harry's aunt) and thus his safety was ensured. Doing this "sealed the charm" (835). Far from being a picture of how Christ saves us through his sacrifice on the cross, as some have claimed (once again, reaching for Christian symbolism), this presents an occult view of what Harry's mother did. Her death was, or became, an act of magic.
We are not magically protected by Christ or by his blood; his blood is not a magical property. Because of what Christ did, we are saved from the second death and redeemed through our faith in Christ. Faith has nothing to do with what Harry's mother did nor with Harry's protection, since he does not understand this protection until the end of the fifth book. And what would Harry have faith in? His mother? No, it would be in the magical protection that continues in her sister's blood after her death. Of course, Harry's mother was not sinless as Christ was; she died for only one person, Harry; she did not plan her death as Christ did; she died to protect Harry's life, not to redeem him from sin; and she did not bodily resurrect and conquer death as Jesus did. The analogy is flawed in the extreme.
As explained in the other two articles, there is a concept of dark and light in the occult called polarity. Generally speaking, magic (sometimes spelled magick) or power is neutral, and one can be on the dark or light side depending on your intentions and how you use the magic or power. The dark and light sides are both parts of the whole and are necessary to each other's existence. Therefore, there is no goal of the light side vanquishing the dark side. The CANA article, "The Dark Side," explains this in depth.
The dark and light sides of a polarity are connected since they are both part of the whole, so there is often a connection between them. This can be seen in the yin-yang symbol, which shows a black dot on the white side (yin on yang) and a white dot on the black side (yang on yin). In the Harry Potter books, Harry and the villain, Lord Voldemort, seem to represent this polarity of dark and light. They are connected in many ways: Voldemort marked Harry with his scar when he tried to kill baby Harry; Harry feels a connection to Voldemort through the scar which burns or hurts when Voldemort is near or is endangering Harry or someone he loves; Harry and Lord Voldemort both speak "parselmouth," the language of snakes; Harry and Voldemort's wands both contain the feather of the same bird; and, most grisly of all, some of Harry's blood is put into Voldemort via a cauldron when Voldemort is being embodied in a ritual in the 4th book, so Voldemort has some of Harry's blood.
These connections show up even more strongly in this book. Not only does his scar burn (178, 275, 474, 586, 728) as a result of this connection (which Dumbledore validates on page 827), but Harry also experiences a psychic connection in what seems to be a case of reading Voldemort's mind (380-382). Snape tells Harry that when he is at his most vulnerable, asleep or relaxed, he is able to share Voldemort's thoughts and emotions (531). Because of this, Snape warns, Voldemort may be able to read Harry's thoughts and control him that way (533). Harry has a dream or vision in which he is a snake who attacks Mr. Weasley (462-463); it turns out that Mr. Weasley really was attacked this way (473-475). Harry has dreams or telepathic visions, in which he seems to be looking into Voldemort's mind, seeing and hearing him (584-586; 727-728). At one point, he seems to be possessed by Voldemort (815-816). Dumbledore tells Harry that when Voldemort tried to kill him as a baby, he inadvertently gave Harry some of his powers, marking Harry "as an equal" (842-843).
The source of power for Harry and Voldemort (and Dumbledore) is the same. Power and magic are, after all, neutral in this view. Voldemort was once at Hogwarts and was an apt pupil. He went over to the dark side, much as Anakin (the young Darth Vader) does in the Star Wars movies. God's word, however, does not mention using magic for bad ends or the dark side of sorcery; God condemns all magical practices, all sorcery, and all spell casting. In reality, there is no dark or light side of magic; there is no white or black magic; there is only magic and it is all against God. Our intentions and beliefs cannot make it good.