'Hagrid almost had to drag Harry away from Curses and Counter-curses (Bewitch Your Friends and Befuddle Your Enemies with the Latest Revenges: Hair Loss, Jelly-Legs, Tongue-Tying and Much, Much More) by Professor Vindictus Viridian.
"I was trying to find out how to curse Dudley."
"I'm not sayin' that's not a good idea, but yer not ter use magic in the Muggle world except in very special circumstances," said Hagrid. "An' anyway, yeh couldn' work any of them curses yet, yeh'll need a lot more study before yeh get ter that level."'
-Harry Potter and the Philosopher's Stone
Harry was disappointed. Hagrid had told him he would be going back to the Dursleys until September first, and even if the awful people left him alone for the month of August out of shock from Hagrid's attack, they surely would be back to their regular abuse by the next summer, and Harry just knew they would blame and punish him for everything Hagrid had done, just as had happened many times whenever a stranger tried to help Harry. He needed to be able to defend himself!
So Harry asked a few more questions later in the day, getting a little more information from each shopkeeper, and then went back to the bookstore for more information. He found out that there was a law called the Reasonable Restriction for Underage Sorcery, and that any wand magic he did away from Hogwarts would be tracked by a spell called the Trace, which would break when he turned 17. The Trace could detect the presence of muggles and wizards nearby, and any active magic performed in his vicinity in the absence of magical adults would trigger it. The presence of muggles nearby would make the offence more serious.
Harry loved his new wand, but it seemed like a trap now that he knew it could be used against him. Might there be a way to break the Trace? Was it on him or on his wand? What if he bought an old used wand? Might there be other magics beside wands that could be used? Harry resolved to find out. He also resolved to study more extensively about potions, which couldn't be tracked as far as Mr. Jiggers the Apothecary knew.
He didn't find anything on used wands until the train ride to Hogwarts when Ron Weasley told him he had his brother's old wand. Apparently these things stayed in the family. Where were Harry's family's old wands? Ron also helpfully told Harry that the Ministry couldn't track enchanted objects. Most of his father's job consisted of monitoring the muggle newspapers, getting tips, and conducting raids to find ordinary objects that didn't behave as they were intended. Most of these objects (biting teapots? Singing soap?), didn't sound very subtle or useful, but surely there were some Harry could get that would help keep the Dursleys off his back. How did one create an enchanted object?
His first week at Hogwarts Harry joined Hermione Granger in the library, asking Madam Pince for information on potions, defence against muggles, and how to enchant objects. Unlike the helpful muggle librarians he had met, she didn't seem to consider helping with research part of her job. She just pointed him toward the relevant shelves and told him to stay quiet.
Harry was very excited about potions class until his first lesson with Professor Snape. The man was the worst teacher Harry had ever had, belittling Harry constantly and refusing to demonstrate or even explain techniques. Harry was very frustrated by this behavior from an authority figure, so he decided to talk to Percy.
The Gryffindor Prefect seemed very busy with his studies, but he also seemed like the best person to know about rules.
"Percy, can I ask you about some of the rules?" This was clearly the best opening, getting Harry a talk with Ron's brother in an out-of-the way corner of the common room.
"Well, my first question is about learning potions. Professor Snape seems very unfair and not a very good teacher. Is there any way to officially protest unfair treatment?"
"I'll pass your complaint to Professor McGonagall, but I'm afraid complaints against Professor Snape have never worked as far as I know. If they did, he would have been fired years ago, and he's only gotten worse over the years."
"The hard thing is, I really want to learn potions. Is there a way to practice the potion ahead of class, or get a tutor? It's just very hard to concentrate and learn in that class." Percy told him that there were in fact brewing labs in the lower levels of Gryffindor Tower that students could sign up to use. Mostly these were used by the upper years, but Harry managed to sign up for a time slot and got several names of potential tutors.
Harry thanked Percy profusely and said he was a great prefect. The next day Harry told Percy he had a few more questions.
"Can you tell me anything about self-defence against muggles? It's just- there's this gang of older boys in my neighborhood, real bullies that have tried to beat me up a few times. I always just run away, but I hate feeling so helpless." Harry made his most pathetic puppy dog eyes, and Percy seemed sympathetic.
"You know the Restriction has exceptions for self defence, right?"
"I do, but I'd rather head off the problem before it can start."
"You really should tell an adult about this, Harry. Surely your relatives can do something to help you feel safer?" Harry strained to not let his real feelings show, and hung his head.
"I wish they could, Percy. It's just that some of the boys have wealthy parents and know they can get away with whatever they want. I'm sure you know the type." He figured Percy might be sensitive about money like Ron was.
Percy nodded. "I'll ask my mum and dad if you can come stay with us over the summer, Harry. I know they'd be glad to have you."
"That's very kind of you. I mean, you've got three annoying little brothers already!" Harry gave him a self-deprecating grin. He had already gotten a promise from Ron to invite him for the summer, but had a feeling that sooner or later he would be forced to go back to Privet Drive. "I was wondering about the Leaky Cauldron, though, and the protections that keep muggles away from places like Hogwarts. They suddenly remember something else they need to do, right?"
"That's right, Harry. Muggle-repelling wards, they're called. A simple enchantment, fairly easy to resist if one knows it's there. They're usually engraved on runestones and placed in buildings, in combination with illusions and other protective enchantments. You're hoping that something like that would keep the bullies from bothering you?"
"Exactly. Is there some way to carry around a short-range muggle repellent, perhaps one that could be turned on and off? I mean, I can't have been the first one to think of it, right?"
"Interesting idea, Harry. I can look into it, and I'm sure Penny and some others would be interested to do some research on the idea. It might make a good NEWT-level project for Ancient Runes."
"It might even be a marketable product if you could mass produce the idea as an amulet or something. I would certainly be willing to subsidize the research."
Percy gave Harry a startled and intrigued look. "I couldn't take your money, Harry."
"Nonsense. I suddenly have spending money I was never told about and if it can help me feel safer at home it's well worth the cost. I would expect a percentage of any profit, so it would be a business deal, free of any obligation."
"I see you're a man of vision, Harry. I'll talk to Penny and some others and get back to you, alright? After all, there might already be something available in that line."
"Thanks again Percy."
After his first potions practice and tutoring session, Harry shared the secret of the underground labs with Hermione Granger and Neville Longbottom, failing to interest the rest of his Gryffindor classmates. Neville was very happy to be able to practice potions without Snape looming, and Hermione was eager to improve her already high performance. Harry mostly wanted to brew some useful potions for his own use. He went through any potions book he could find or borrow, listing the most useful ones, along with their expected skill level, time requirement, and rarity of ingredients, and prioritized the best ones for him.
There were a large number of potions with flashy and obviously magical effects which Harry passed over immediately. He didn't want the Dursleys to know they were being affected by magic. The most useful ones he found were draughts to alter emotions or states of mind, such as confusion, forgetfulness, drowsiness, euphoria, despair, and sleep. Could he simply put the Dursleys to sleep for two months? He idly looked at the many descriptions of love potions, but discarded the idea. There were non-romantic options such as Gregory's Unctuous Unction, which made the drinker think the giver was his best friend, but Harry didn't actually want the Dursleys to love him anymore, in fact the idea repulsed him. Also, if he missed a dose, they would realize what had happened when the effect wore off and might become violent. There was one passage that got his attention, though, listed as an antidote to love potions:
"...The Hate Potion is also recommended for witches and wizards who are emotionally attached to a person who does not return their feelings. Although not guaranteed to cause the drinker to completely lose their feelings for a loved one, it does show the drinker the person's worst traits and habits, and so discourages them from creating a relationship with that person." *
Wish I'd taken that potion when I first went to live with the Dursleys, he thought in disgust. It would have saved me a lot of heartache from trying to fit their definition of normal so they would finally love me. Not that he had ever really loved them, he was sure, but as a child who was only shown how they treated each other as an example of love, he had craved any positive attention. They love each other because they think they're normal, but in truth their family is the furthest thing from it, he thought. If only they could be shown how awful they really are, or how awful each other are... The Hate Potion was definitely something to consider.
*Quoted from Harry Potter wikia. I actually went through lists of potions on this and other sites looking for the most useful ones. The Hate Potion was introduced in the Daily Prophet newsletters written by J.K. Rowling and produced by Bloomsbury for their Harry Potter fan club.
A lot of fanfics have Harry go on a spree at Diagon Alley, buying all sorts of useful things, but there's also his whole first year at Hogwarts, where he could be getting a lot of advice from older students who respect or want to benefit from his reputation, or ordering products by owl.
The Trace is one of the most confusing plot devices in the Harry Potter series. We don't know how it works exactly, but I've tried to come up with an explanation. I think it is placed on first year students either when they buy their wands or when they arrive at Hogwarts, and marks them as underage. It can detect the presence of muggles and adult magic users. Something in the Ministry also monitors the locations around where muggle-raised students live, and reports violations when the Trace is triggered there.
I've always been annoyed that Harry in the books never even tried to use indirect magic to make his life at the Dursleys' easier, or get back at them for their cruelty. Is he just not vindictive? Check the quote at the beginning of the story. At the very least, he could have used his cloak to sneak around. We know from the flying car incident that enchanted objects are not detected, and there is some evidence for potions being undetected too. Also, the idea that non-Slytherin students wouldn't have secret potions labs and tutoring systems is improbable.