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While the triumph of good over evil was the foundation of the Harry Potter series, it was the magical world of wizards and witches that captivated audiences. Harry went from being an ordinary orphan boy in London to living a life beyond his imagination at Hogwarts School of Witchcraft and Wizardry. Adventure and thrills were a big part of Hogwarts, but it was, first and foremost, a school that taught young wizards magic.
Hogwarts had some seriously fascinating subjects, which were a big part of its appeal. While young readers dealt with Arithmetic and English in school, they could read about Transfiguration, Defence Against the Dark Arts, and Potions in Harry Potter. Many of these wizarding classes made it to the movies, but several were left out of them, either for brevity or because they didn't translate well to the screen. These were the wizarding subjects that didn't make it to the Harry Potter movies.
A subject that never quite made it to the movies, Arithmancy was actually quite an interesting avenue of study. Hermione had taken Arithmancy in her third year, which made sense because the class was quite an advanced one. It involved studying magical numbers to predict the future, but it was an exact science in its own way, involving numerical charts to be made by students.
Arithmancy was never really shown as a class in the movies, but Professor Septima Vector did appear in Harry Potter and the Sorcerer's Stone, unnamed verbally but present in the movie's credits. It is possible that since Arithmancy was an elective subject that witches and wizards had to choose in their Third Year, it didn't make it to the movies. It was one of the subjects that Hermione used the Time-Turner to attend.
Another subject that got mentioned in the movies but never shown was Study of Ancient Runes. Again, this was a subject that Third Year students could opt for. It delved into the ancient alphabet used by Bronze/Iron Age wizards called Runes, which were particularly difficult to decode. It was a difficult subject, and even Hermione made a mistake in one of her Ancient Runes translations in her OWL exams.
Taught by Hogwarts' Professor Bathsheda Babbling, Ancient Runes was mentioned verbally by Hermione when she compared it to the controversial subject Divination, and Sirius Balck's prison mugshot had Runes on it. The class itself never made it to the screen, and only fans wouldn't know of it.
History of Magic was considered largely boring by Harry and Ron, and Harry hadn't cracked open the eponymous textbook more than once. However, this subject proved to have a strong connection with Harry's life. Fans would remember Bathilda Bagshot from Harry Potter and the Deathly Hallows, whom Harry and Hermione had a lethal encounter with at Godric's Hollow. Bagshot was the author of the History of Magic textbook.
Even the professor who taught the subject had an interesting story. Professor Cuthbert Binns taught his class till the day he died, but when he slumped over his desk, his ghost continued teaching. Thus, Cuthbert Binns was a ghost by the time Harry came to Hogwarts. Learning about Wizarding Wars and rebellions may not be intriguing for Hogwarts students, but fans would have loved to know more.
A subject that was actually very similar to the Muggle world was Astronomy, which was the study of stars and planets and their movements in outer space. Taught by Professor Sinistra, Astronomy lessons didn't make it to the screen, but the Astronomy Tower was shown in one of the most pivotal scenes in Harry Potter and the Half-Blood Prince -- Dumbledore's death scene.
Astronomy was also a compulsory subject for Hogwarts students from the First to Fifth Year, after which it became optional. Considering how important Astronomy was, it is surprising that the classes weren't depicted in the movies. It also was a confluence of Wizarding and Muggle culture, which would have been interesting to watch.
The most well-known mention of Alchemy in Harry Potter is the Sorcerer's Stone, which was developed by noted alchemist Nicolas Flamel. Book readers would know that Alchemy was also an actual subject at Hogwarts, available as an elective for Sixth and Seventh Year students to pursue. This subject dealt with the nature of the elements: air, water, fire, and earth. It also studied their transmutable qualities, a common example of which is turning things into gold.
Nicolas Flamel was able to elongate his life unnaturally by using Alchemy. The Sorcerer's Stone could turn anything into gold and also produced the Elixir of Life. This elixir could render the drinker immortal.
Muggle Studies was a subject that helped inform wizards and witches about the Muggle world, especially those who had not ever been in contact with Muggles. Arthur Weasley's fascination for Muggle-made things was depicted in the movies, but the actual class was not shown. However, a tragic event regarding the subject and its Professor was in Harry Potter and the Deathly Hallows: Part 1.
The hatred against Muggle-borns was so high during Voldemort's second reign that the Dark Lord had a problem with Muggle Studies being taught at Hogwarts. In addition to abolishing the subject, he also kidnapped and tortured Professor Charity Burbage. When she became useless to him, Voldemort killed her mercilessly.
The amazing Wizarding ability to teleport from one location to another in a few milliseconds, known as Apparition, was a mainstay in the Potter movies. However, it is not widely known that the skill was not something that was acquired without training. Hogwarts was where young Wizards and Witches learned how to Apparate every Saturday morning from Wilkie Twycross, who was not a professor but a ministry official. For this period, the Anti-Apparation Charm was removed from Hogwarts grounds.
This Wizarding class was not an official part of Hogwarts curriculum, but one by the Ministry, which cost 12 Galleons to attend. The motto that Twycross told his students to follow was "The Three Ds: Destination, Determination, and Deliberation." After they learned, wizards could take the Apparition test.
The Harry Potter franchise follows the adventure of a young boy introduced a whole new world of magic, mayhem and darkness. Traversing the obstacles in his path, young Harry's rise to heroics pits him against Lord Voldemort, one of the most dangerous wizards in the world and all his minions.