McGonagall is Deputy Headmistress of Hogwarts and one of Dumbledore's staunchest supporters. She is a stern, strict witch with little patience for those who do not follow the rules. She took over as Headmistress when Dumbledore was temporarily removed from his post by the governors after a string of attacks by an unknown monster on students (CS14).

She is not afraid to punish students of her own house, Gryffindor, and even take points away from them if it means losing the House Cup. In fact, in her zeal she has taken excessive points from Gryffindor students (e.g.50 points per Gryffindor student who was out of bed and wandering the castle right after taking only 20 points away from a Slytherin student who was guilty of the same infraction). Gryffindor students have remarked that they wish she would favor them the way that Snape always seems to favor Slytherins (SS8). 

McGonagall is an Animagus who can turn into a tabby cat at will. When a cat, she has markings around her eyes similar to the square glasses she wears (SS1).

McGonagall teaches Transfiguration classes at Hogwarts. She considers other forms of magic to be somewhat less elegant and more simplistic than Transfiguration. She is famous for giving vast amounts of homework (SS8).

McGonagall and Hermione seem to have a lot in common, a certain strictness about rules for one thing. Both have been described as being particularly clever. McGonagall arranged for Hermione to use a Time Turner in her third year to take additional classes (PA5).

McGonagall occasionally shows her softer side. When Harry and Ron told her that they were going to the infirmary to visit Hermione, who had been Petrified, she gave them permission with a tear in her eye (CS16). She cried when she learned that Lily and James Potter had been killed (SS1). She felt bad about treating Peter Pettigrew sternly when she thought that he'd died to capture Sirius Black (PA10).

McGonagall wears emerald green robes (SS7). Her night dress is a tartan bathrobe and hairnet (SS14, PA13). She carries a lace handkerchief (SS1). She disapproves of "letting her hair down," although she did wear a top hat at the Christmas party of 1991 and even giggled and blushed when a rather tipsy Hagrid kissed her on the cheek (SS12). At the Yule Ball of 1994, she wore dress robes of red tartan and arranged a rather ugly wreath of thistles around the brim of her hat. She danced with Ludo Bagman (GF23).

McGonagall is quite a Quidditch fan. She is an enthusiastic supporter of her house team. When she saw Harry Potter catch a Remembrall with a diving grab in midair, she immediately made him the team Seeker and arranged for him to have a broomstick, which was against the rules. (SS)

McGonagall, Minerva
hair: 
black, pulled back into a bun (SS7)
eyes: 
square glasses, beady eyes
distinguishing features:
an Animagus capable of turning into a cat; rarely smiles (SS8)
age: 
approx. 70 (Sch2) (born c. 1920)
House: 
Gryffindor (c. 1931-38)
field: 
Transfiguration
office: 
first floor (up the main staircase, down a corridor)
interests:
she is very keen on Quidditch