Disciplines of Transfiguration and Transmutation
When new students are introduced to magic, the first disclaimer they receive is how devilishly hard transfiguration is. This is not an exaggeration on the part of the teacher, nor is it because of the age or lack of skill of the student.
Transfiguration is hard because physical objects are very stubborn. They spent their entire lives as a certain thing and they're very set in their ways. A lemon juicer has probably lived a happy, successful life as a kitchen implement and resents your presumptive attempt at turning it into a sextant. This is a good thing, for the most part. Most people who are riding on a broom stick wouldn't want the broom to get ideas about turning into a hat rack and making an unexpected transformation while flying a mile over the Aral Sea.
This resolution extends to all the object's individual properties, from color to size to texture. This means transforming an object little by little isn't any easier than going from Shape A to Shape B in one step. This is one of the few areas where breaking the problem down into smaller parts makes the task harder.
In addition to the inherent difficulty, there are some things you simply cannot transfigure for any reason or at any cost. These limits were researched in depth, and carefully described for posterity by Elvendor Gamp, noted Alchemist who, during the Roman occupation of Scotland, transformed Hadrian's Wall from a 15-foot tall blockade to a 3-foot high sheep fence. This impressive feat is famous for weakening Rome's grasp of England and driving the emperor Hadrian insane with confusion. In honor of his research and subversion, these limits are refered to as Gamp's 5 Exceptions to Elemental Transfiguration.
Most young people, studying magic for the first time, believe it is merely a matter of time and study before they can conjure up houses, money, true love, and live comfortably; happily ever after, if you will. They are disappointed that this is precluded from the outset, but come to accept that this arrangement does more good than harm. Limitations hold people back, but sometimes, what they hold back, is certain disaster.
The first exception is food. Food cannot be conjured or transfigured from a non-food substance. This limitation is often cursed by hungry witches or wizards who are either lost in the wilderness or don't feel like walking to the kitchen. There are work-arounds for this problem. If food is already present it can be duplicated. A clever witch can make a bagel last for a month, though one can't imagine anyone willing to try. The reason for this appears to be the complexity of food. What we've always simply labeled as 'meat' or 'grain' is actually complex chains of acids, carbohydrates, and salts. These are concepts that can barely be spelled let alone spelled (letters and magic, respectively). In the case of duplication, the magic already has a rubric, so to speak, to work off of.
The second exception is metal. Metal is, proportionally, even more stubborn than food. It can't be conjured, transfigured, or even vanished. This has been an underlying theme in the struggle between muggles and wizards. It started so long ago when humans began designing an economic system, deviating from their long history of eating raw meat and living in trees. Gold had been discovered, but had no practical application. It was soft; useless for tools or protection, but by this same token, it could be easily bent into artistic shapes. By dint of being pretty, it was adopted as a currency. With the advent of currency, people could devote themselves to industries besides growing food and avoiding tigers. This led to a boom in the variety of goods and services being provided. The magical people of the time got the brilliant, highly unethical idea of conjuring gold, buying everything they needed, and never working again. They failed to produce actual gold, a metal, so they settled for the next best thing: making rocks look like gold. Their deception was discovered and they were dealt with harshly. This began a long tradition of wizards and witches being mistrusted and subsequently stoned to death. The issue was compounded when metals were used in the production of weapons, which increased slaughtering efficiency and couldn't be magically vanished. The advent of ballistics allowed for ranged attacks, which were previously exclusive to wand wielding persons. Magic can alter the shape and properties of metals, a discipline known as Alchemy. The Goblin's have the market cornered on Alchemy. They are famous for imbibing weapons and jewelry with magical properties. The Sword of Godric Gryfindor is famed for being able to appear in his clutch whenever he needed it. Some legends say it was so sharp you could cut yourself just by looking at it. The ultimate goal in the study of alchemy is the production of the Philosopher's Stone, an object of great purity that can turn any metal into gold and produce the Elixir of Life. How the Elixir of Life relates to magical metallurgy is somewhat unclear, but alchemists are content to just roll with it.
The third exception is slood. Slood is totally immune to the effects of any kind of magic. Slood cannot be summoned, duplicated, transfigured, conjured, charmed, cursed, vanished, engorged, enchanted, jinxed, amplified, switched, locomoted, levitated, inflated, pasteurized, calibrated, shrunken, murdered, bribed, elected, lubricated, synchronized, blessed, liberated, irrigated, canonized, bowdlerized, frozen, sublimated, inveigled, consecrated, melted, galvanized, alphabetized, calibrated, leavened, unleavened, coalesced, demonized, anglicized, pixilated, contained, compounded, concocted, corrected, criticized, keratinized, coalesced, karate-chopped, floccinaucinihilipilificated, or otherwise effected by magic.
The fourth exception is life. Life cannot be created by magic, as discussed earlier in the fundamental laws of magic. However, this rule is so important, it needed repeating. A skilled witch or wizard can turn conjure canaries out of thin air. These canaries, when scrutinized, aren't made of actual flesh, and have a strangely laid back attitude to being cut open. When left to their own devices long enough, they will stop moving all together. They are merely a cheap imitation of life. Unlike with food, life cannot be duplicated. Any attempt to do so would be … ugly. Living things can be altered by magic. Every few years, young wizards get the impression that growing long facial hair is cool. It isn't, but producing an impressive beard is a simple spell. There are many such cosmetic spells; easy to perform, generally not fatal. Though again, facial hair, not cool.
The fifth exception is time. As anyone who has ever sat at the bedside of a dying loved one can attest, you can't create more time. You can't steal time from someone else. It can't be slowed or hastened. Time is unforgiving, unrelenting, unreasonable, and punctual. Time is the most fair of all commodities. It passes at the same rate in all places for all people. Some people don't have as much time as others, but what can you do. Honestly, if you wanted to transfigure time, there's no consensus on which direction you'd even point your wand. On the other hand, you can make as much space as you want, the fabric of reality is strangely elastic in that respect. This discovery was, and still is, widely celebrated. No matter the size of the cottage the witch or wizard owns, they can fit 3 full bathrooms.
For a long time, it was believed that only solids could be transfigured. This was disproved in the year 1640, after years of tireless effort, by the Sorcerer Cridh of Irelend, who transfigured water into whiskey. Cridh died a week after his landmark discovery of severe liver failure. He drank so much his liver abandoned ship. He was so drunk his coffin got tipsy. He was so soused his corpse still hasn't decayed. He had so much liquor in him after they buried him the ground threw up.
This is a reminder of the seventh law of magic: Just because you can, doesn't mean you should.