'Lumos' was the first spell he used willingly outside Hogwarts before his 3rd year!
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There is no mention of anything called velodromes in the Harry Potter series.If you mean Hogwarts, the first spell he learned was Wingardium Leviosa.
When Voldemort used the Elder Wand (of which Harry is actually the true master) to cast the spell "Avada Kedavra" and Harry cast "Expelliarmus", Voldemort's curse rebounded killing Voldemort. And the Battle Of Hogwarts was won...
Details or the name of the spells are not known; it is supposed to protect Harry from Voldemort while he lives at his mother's relations' house. And he is under-age. And he is not in Hogwarts.
Petrificus totalis
you go to the main section of Hogwarts where there are two flights of stairs and you go up the left on and that Door is the library. *please note you need a certain spell to open the library*