This is possibly the most famous book to take its title from a Shakespeare play – in this case, The Tempest. In Act V Scene I, Miranda declares:
How beauteous mankind is! O brave new world
That has such people in 't!
She says this when encountering new arrivals to her island for the first time in her life, and the 'savage' John repeats it when gazing at the corrupt, hedonistic society portrayed in Huxley's 1932 novel. Huxley was a big fan of Shakespeare and quoted him in two more famous book titles, namely Tomorrow and Tomorrow and Tomorrow (1956) and Mortal Coils (1921), from Macbeth and Hamlet respectively. Both are part of famous soliloquies; Hamlet's in particular is the 'to be or not to be' speech.
Tomorrow, and tomorrow, and tomorrow,
Creeps in this petty pace from day to day,
To the last syllable of recorded time;
And all our yesterdays have lighted fools
The way to dusty death. —Macbeth, Act V Scene V
For in that sleep of death, what dreams may come,
When we have shuffled off this mortal coil,
Must give us pause. —Hamlet, Act III Scene I