(German) literally Superman. The Übermensch is a philosophical concept introduced by Thomas Carlyle in 1840 in his book On Heroes, Hero-Worship and the Heroic in History. The book proposed that "The history of the world is but the biography of great men," and that each era of human civilization was defined by the abilities and religion of its Übermensch. Used this way, Joyce would be advocating that his heros are the defining force behind their society.
However, Joyce is also clearly referring to another work, and Mulligan speaks its title: Thus Spake Zarathustra. This references the Übermensch concept as discussed by Friedrich Nietzsche in 1883 in his book Also Sprach Zarathustra. Nietzsche used the term to describe a human being who has successfully transcended or surpassed human nature, one who has freed himself from Christian morality and spiritualism, one who has evolved to a higher state.