This is what I pulled together from different sources.
Studies by Year:
A first year is a student at Hogwarts School of Witchcraft and Wizardry who is new to Hogwarts and in their first year of magical education. There are usually ten first-years per house (five boys, five girls), leaving a total of forty students per year. First years are typically eleven to twelve years of age. First years arrive at the castle by crossing the lake with the Keeper of the Keys in boats separate from the older students. They are not allowed on their broomsticks unless they are attendingFlying class. First year classes consist of Potions, Herbology, Defence Against the Dark Arts, Transfiguration, History of Magic, Astronomy, Charms, and Flying.
A second year is a student at Hogwarts School of Witchcraft and Wizardry who is in their second year of magical education. Second years are typically twelve to thirteen years of age, unless a student had to repeat the second form. The second year is the first year in which students are allowed, when arriving, to go with the rest of the school in the school carriages pulled by Thestrals up to the castle. Second year classes consist of Potions, Herbology, Defence Against the Dark Arts, Transfiguration, History of Magic, Astronomy and Charms. Unlike first years’, the second-years’ timetable does not include Flying, although they are allowed to bring their own broomsticks.
A third year is a student at Hogwarts School of Witchcraft and Wizardry who is in their third year of magical education. Third years are typically thirteen to fourteen years of age. The third year is an important one for students, as it is the first year that they are permitted to sit elective courses. Third year classes consist of Potions, Herbology, Defence Against the Dark Arts, Transfiguration, History of Magic, Astronomy, Charms, and the two or more electives the student chose the previous year. Third years are permitted to go to Hogsmeade during certain weekends if they have a signed permission form from their parent/guardian.
A fourth year is a student at Hogwarts School of Witchcraft and Wizardry who is in their fourth year of magical education. Fourth years are typically fourteen to fifteen years of age. The fourth form is almost identical in its structure to the third; students sit two or more elective courses in addition to the core classes, and are allowed in Hogsmeade during selected weekends. Fourth year classes consist of Potions, Herbology, Defence Against the Dark Arts, Transfiguration, History of Magic, Astronomy, Charms, and two or more electives. Although, fourth years typically get more work than third years, to prepare for their O.W.L.s.
A fifth year is a student at Hogwarts School of Witchcraft and Wizardry who is in their fifth year of magical education. Fifth years are typically fifteen to sixteen years of age. The fifth year is enormously important for students, due to the fact that it is the year in which they must sit their O.W.L. exams, which will determine what N.E.W.T. courses they will be permitted to take later on in their education. O.W.L.s determine what jobs they can apply for in their future careers. The fifth year is also the year in which students receive career counseling from their Heads of House. It is during this meeting that they will be advised as to what N.E.W.T.-level classes they should take in order to qualify for their desired career. Fifth year classes consist of Potions, Herbology, Defence Against the Dark Arts, Transfiguration, History of Magic, Astronomy, Charms, and two or more electives. Before the beginning of the year, one boy and one girl are selected by the Headmaster from each House to become prefects.
A sixth year is a student who is in his or her sixth year of magical education at Hogwarts School of Witchcraft and Wizardry. Sixth years are typically sixteen to seventeen years of age, although some may be older, if they have had to repeat a year like Marcus Flint did.
The sixth year is the first year in which students sit N.E.W.T.-level classes. Based on their O.W.L. scores, and depending on the minimum requirements of the professor teaching the subject at that time, students are allowed to sit any number of classes as long as they meet said requirements. If the student doesn’t meet those requirements, they cannot attend the N.E.W.T.-level classes, having to repeat the O.W.L.-level classes and the fifth-year exams. While students do have the opportunity to choose whether they wish to continue in particular subjects, those who begin studying N.E.W.T.-level subjects in their sixth year are expected to carry on with the subject into the seventh year, and sit the N.E.W.T. exam in that subject. Sixth year students are initially excited to have more free time, but this extra time is intended to help them study and do homework, as many, if not all, teachers assign more homework and give more difficult lessons in their N.E.W.T.-level classes. Sixth years may also elect to take part in Apparition lessons for a fee of twelve Galleons.
A seventh year is a student at Hogwarts School of Witchcraft and Wizardry who is in their seventh and final year of formal magical education. Seventh years are typically seventeen to eighteen years of age, although some may be older if they have had to repeat a year. The seventh year contains the most important exams given at Hogwarts - the N.E.W.T.s. Students conclude their N.E.W.T.-level studies in the seventh year, at the end of which they sit the N.E.W.T. exam pertaining to each of their subjects. A student in the seventh year would have the same schedule he or she had in the sixth year, and would sit only those classes in which they received O.W.L.s meeting the minimum requirement of the professor for that subject. However, not all students take N.E.W.T.s, as some occupations require only O.W.L.s.
Every year, a male and female seventh year are appointed Head Boy and Head Girl. In most cases the Headmaster selects the Head students from the seventh year prefects. However students that have never been prefects, for example James Potter, can still be selected.
Studies at Hogwarts
Transfiguration is essentially the art of changing the properties of an object. Transfiguration is a theory-based subject, including topics such as "Switching Spells" (altering only a part of some object, such as giving a human rabbit's ears); Vanishing Spells (causing an object to completely disappear); and Conjuring Spells (creating objects out of thin air). It is possible to change inanimate objects into animate ones and vice versa – Minerva McGonagall, the class's teacher, transfigures her desk into a pig and back in Philosopher's Stone.
Defence Against the Dark Arts
Defence Against the Dark Arts, commonly shortened to D.A.D.A., is the class that teaches students defensive techniques to defend against the Dark Arts, and to be protected from Dark creatures.
The subject has an extraordinarily high turnover of staff members – throughout the series no Defence Against the Dark Arts teacher has retained the post for more than one school year. During the period the story takes place, the class is taught by Quirinus Quirrell (book one), Gilderoy Lockhart (book two), Remus Lupin (book three), Bartemius Crouch Jr impersonating Alastor "Mad-eye" Moody (book four), Dolores Umbridge (book five), Severus Snape (book six), and Amycus Carrow (book seven). Hagrid suggests in Harry Potter and the Chamber of Secrets that "They're startin' ter think the job's jinxed. No one's lasted long for a while now." In Half-Blood Prince, Dumbledore suggests that Voldemort cursed the position because his application for it was rejected. The existence of the jinx was eventually confirmed by Rowling. The position had also been coveted by Snape, but he was denied the position as well. Snape was finally appointed D.A.D.A. professor in Half-Blood Prince. Rowling announced in an interview that once Voldemort had died, the jinx he placed on the office was lifted and a permanent professor had been teaching the subject between the end of Deathly Hallows and the epilogue, set nineteen years afterwards. Furthermore, she imagines that Harry Potter occasionally comes to the class to give lectures on the subject.
Charms is the class that teaches how to develop incantations for the uses of bewitchment. Rowling has described Charms as a type of magic spell concerned with giving an object new and unexpected properties. Charms classes are described as notoriously noisy and chaotic, as the lessons are largely practical. Many of the exposition sequences in the books are set in Charms classes, which are on the second floor of Hogwarts. The class is taught by Professor Flitwick.
Potions is described as the art of creating mixtures with magical effects. It requires the correct mixing and stirring of ingredients at the right times and temperatures. As to the question of whether a Muggle could brew a potion, given the correct magical ingredients, Rowling has said, "Potions seems, on the face of it, to be the most Muggle-friendly subject. But there does come a point in which you need to do more than stir." Snape's lessons are depicted as unhappy, oppressing times set in a gloomy dungeon in the basement of the castle, whilst Slughorn's, who replaces Snape as Potions Master, are shown as more cheerful and even fun at times.
Astronomy classes take place in the Astronomy Tower, the tallest tower in Hogwarts, and are taught by Professor Aurora Sinistra. Lessons involve observations of the night skies with telescopes. No astronomy lessons are shown in the books, but they are frequently referenced. Rowling describes one of Harry's Astronomy exams in Harry Potter and the Order of the Phoenix. Also, bits of the Astronomy Tower are seen throughout the film series, such as HP2 and HP3, and featured in The Half-Blood Prince, as the place where Dumbledore died, and seen in The Deathly Hallows. Known student homework activities include learning the names of stars, constellations and planets, and their location, movements, and environments.
History of Magic
History of Magic is the study of magical history. Cuthbert Binns' lessons are depicted as some of the most boring at Hogwarts. They are only lectures, given without pause, about significant events in wizarding history. Topics have included goblin rebellions, giant wars, and the origins of wizarding secrecy. This is the only class at Hogwarts that is taught by a ghost, as the professor never noticed he had died and simply continued teaching as if nothing had changed.
Herbology is the study of magical plants and how to take care of, utilise and combat them. There are at least three greenhouses described in the books, holding a variety of magical plants of varying degrees of lethality. Herbology is also the only subject Neville excels in. The epilogue to Deathly Hallows explains that he later replaces Professor Sprout as the Herbology teacher.
Arithmancy is a branch of magic concerned with the magical properties of numbers. As neither Harry nor Ron take this class, almost nothing is known about it. It is, however, a favourite subject of Hermione. Arithmancy is reportedly difficult, as it requires memorising or working with many charts. The subject is taught by Professor Septima Vector.
Study of Ancient Runes
Study of Ancient Runes, more commonly known as Ancient Runes, is a generally theoretical subject that studies the ancient runic scripts. Because only Hermione studies it, little else is known about this subject. It is taught by Professor Bathsheda Babbling.
Divination is the art of predicting the future. Various methods are described, including tea leaves, fire omens, crystal balls, palmistry, cartomancy (including the reading of conventional playing cards and the tarot), astrology, and dream interpretations. Divination is described by Professor McGonagall as "one of the most imprecise branches of magic". Supporters of the subject claim that it is an inexact science that requires innate gifts like the "Inner Eye". Those opposed claim that the subject is irrelevant and fraudulent. Harry is first taught Divination by Professor Trelawney, and then later by Firenze after Trelawney is sacked by Dolores Umbridge in Harry's fifth year. In the sixth (and presumably seventh) year, Firenze and Professor Trelawney teach Divination.
Care of Magical Creatures
Care of Magical Creatures is the class which instructs students on how to care for magical beasts. Classes are held outside the castle. In Harry's first two years, the class is taken by Professor Silvanus Kettleburn who then retires "in order to enjoy more time with his remaining limbs". Dumbledore then recruits the gamekeeper Rubeus Hagrid to accept a teaching position along with his gamekeeping duties. Although Hagrid is obviously very experienced and knowledgeable, he doesn't "have a normal person's view of what's dangerous", and so consistently misjudges the risk that the animals he uses in his lessons pose to his students, which sometimes results in chaos. When Hagrid is absent, his lessons are taken over by Professor Grubbly-Plank, a witch and an acquaintance of Dumbledore's.
Muggle Studies is a class taught by Charity Burbage which involves the study of the Muggle (non-magical) culture "from a wizarding point of view." The only need for witches and wizards to learn about Muggle ways and means, is to ensure they can blend in with Muggles while needing to do so (for example, at the 1994 Quidditch World Cup). As the class is only mentioned as being taken by Hermione, and for just one year, little is known about its curriculum.
In the opening chapter of the final book, Voldemort murders Professor Charity Burbage because she portrays Muggles in a positive light and is opposed to limiting wizardry to only people of pure-blood origins. For the rest of the academic year covered by Deathly Hallows, the Death Eater Alecto Carrow teaches Muggle Studies. However, her lessons (which are made compulsory) mainly describe Muggles and Muggle-borns as subhuman and worthy of persecution.
Alchemy classes are not mentioned in the Harry Potter series; however, Rowling has used Alchemy as an example of a 'specialised' subject offered when there is sufficient demand. Alchemy is a philosophical tradition searching for the philosopher's stone, which is said to have the power to turn base metals into gold and to contain the elixir of life, which makes or keeps the drinker young and immortal. As mentioned in Harry Potter and the Philosopher's Stone, Nicholas Flamel created a Philosopher's Stone, but it was destroyed at the end of Harry's first year.
Flying is the class that teaches the use of broomsticks made for the use of flying and is taught only to Hogwarts first years by Rolanda Hooch. The subject is the only one that requires physicality. The only flying lesson depicted in the Harry Potter series is in Harry Potter and the Philosopher's Stone.
Apparition is the magical form of teleportation in the Harry Potter series. Apparition is an optional class for those in the sixth and seventh years. The lessons are taught by Wilkie Twycross, a Ministry of Magic Apparition Instructor, in Harry's sixth year at Hogwarts. In the wizarding world, performing Apparition requires a license and may only be legally performed by people over seventeen years of age. The described reason for the restriction is that Apparition is dangerous if done improperly: insufficient concentration may lead to body parts being left behind in an unfortunate side-effect known as splinching; Twycross explains this as happening when a witch or wizard is insufficiently determined. Because of the dangers of Apparition, most witches and wizards don't bother with it; they prefer the slower but safer methods, such as broomsticks.
In Harry Potter and the Deathly Hallows, it is mentioned that Voldemort needed to fly close enough to Hogwarts to Apparate to the grounds, therefore one can assume Apparition requires a certain distance between the witch or wizard Apparating and the desired destination.
Underage witches and wizards can Apparate with a witch or wizard that is licensed in Apparition. This is called Side-Along Apparition and is used by Harry in Half-Blood Prince. Those Apparating can also be steered by another witch or wizard. Both of these require holding on to the other witch or wizard, though Side-Along Apparition requires a firmer grip.
Magical enchantments on Hogwarts castle and grounds prevent Apparition and Disapparition inside the castle; however it is explained in Half-Blood Prince that these protections are temporarily relaxed within the Great Hall for short periods to permit students to practice. Students are warned, though, that they will not be able to Apparate outside of the Great Hall and that it would be unwise to try.