A list of the past and present Hogwarts staff and what they teach/taught.
Professor Binns – History of Magic
Charity Burbage – the Muggle Studies professor in years 1-6
Alecto Carrow – Muggle Studies professor in year 7
Amycus Carrow – Defense Against the Dark Arts professor in year 7
Albus Dumbledore - Previous Transfiguration; headmaster
Argus Filch – caretaker
Firenze – the Divination teacher during part of year 5 and the helper in year 6
Filius Flitwick – Charms teacher, head of Ravenclaw house
Wilhelmina Grubbly-Plank – the Care of Magical Creatures teacher during part of Harry’s 4th and 5th years
Rubeus Hagrid – keeper of grounds and keys; Care of magical Creatures
Madam Hooch – first years flying instructor; Quidditch instructor
Professor Kettleburn – the Care of Magical Creatures teacher before Harry’s 3rd year
Gilderoy Lockhart – the Defense Against the Dark Arts teacher in Harry’s 2nd year
Remus Lupin – the Defense Against the Dark Arts teacher in Harry’s 3rd year
Neville Longbottom – the Herbology teacher as of the epilogue of Deathly Hallows
Minerva McGonnagal – the Transfiguration teacher; the head of Gryffindor house
Alastor Moody – the Defense Against the Dark Arts teacher in Harry’s 4th year
Irma Pince – the Hogwarts librarian
Poppy Pomfrey – the nurse
Professor Quirrel – the Defense Against the Dark Arts teacher in Harry’s 1st year
Professor Sinestra – the Astronomy teacher
Horace Slughorn – the Potions professor in Harry’s 6th year
Severus Snape – the Potions teacher in Harry’s 1st -5th years, Defense Against the Dark Arts teacher in Harry’s 6th year, Headmaster in 7th year, head of Slytherin house
Sybil Trelawney – the Divination professor
Ponoma Sprout – The Herbology teacher, head of Hufflepuff house
Delores Umbridge – the Defense Against the Dark Arts professor in Harry’s 5th year
Professor Vector – Arithmancy