Mary has meals at Oxbridge University and Fernham College that show her how different men's and women's experiences are. (Plus some unpleasant encounters at Oxbridge.) This sets the stage for her investigation of why it's so hard for women to write.
Mary visits the library to solve this little problem. Too bad that it's useless: all the books are written by angry dudes who seem way too interested in asserting their own superiority. If she can't trust the guys who write the books, how is she going to learn anything about women and writing?
Things turn a corner when Mary realizes that writers need to let the male and the female parts of their minds out to play if they want to write well. No more "Girls rule; boys drool" (or the other way around)—it's time to grow up.
Woolf takes off the Mary Beton mask and considers a few possible objections to the ideas she just put forth. Now that Woolf has gotten her ideas across, it's time look at the gory details.
We go out on a positive note, when Woolf urges women to write and write so that a future incarnation of Judith Shakespeare can be born. All right! Someone hand us a pen!