In the third year, students were able to select from a more diverse list of courses. As a result, not all students shared the same curriculum.
For example, Harry added only Divination and Care of Magical Creatures from the previous year.
Most important of all, he had to buy his new schoolbooks, which would
include those for his two new subjects, Care of Magical Creatures and
Hermione, on the other hand, had quite a few more:
"Well, I'm taking more new subjects than you, aren't I?' said
Hermione. "Those are my books for Arithmancy, Care of Magical
Creatures, Divination, the Study of Ancient Runes, Muggle Studies --"
The courses offered were (elective courses in bold):
Not all of these classes involved spells or potions.
The main textbook is the Standard Book of Spells, Grade 3.
According to Potterwiki
This is the first book in The Standard Book of Spells series whose
contents will not be viewable on Pottermore.
Also according to the wiki, the spells for the third year can be found in Harry Potter and the Prisoner of Azkaban (video game), but include the Patronus Charm. So they should perhaps be taken with a grain of salt. This is not canon, since it is all from the video game, and the textbook is not visible on Pottermore.
In any case, the spells are:
Apparently this transfigures objects into dragons.
Apparently this transfigures objects into rabbits.
Lumos Duo Charm
Seize and Pull Charm
Apparently this transfigures objects into mice.
The following spells are backed up by book quotes, and are canon.
Flitwick taught Cheering Charms:
"You're late, boys!" said Professor Flitwick reprovingly as Harry
opened the classroom door. "Come along, quickly, wands out, we're
experimenting with Cheering Charms today, we've already divided into
Professor Lupin taught the Boggart-Banishing Spell:
"The charm that repels a boggart is simple, yet it requires force of
mind. You see, the thing that really finishes a boggart is laughter.
What you need to do is force it to assume a shape that you find
"We will practice the charm without wands first. After me, please ...
Technically, he also taught another spell:
"This is a useful little spell, he told the class over his shoulder.
"Please watch closely." He raised the wand to shoulder height, said,
"Waddiwasi! "and pointed it at Peeves.