Overman
The translation of the German word Ubermensch and the goal of humanity. The overman is someone who has overcome himself fully: he obeys no laws except the ones he gives himself. This means a level of self-mastery that frees him from the prejudices and assumptions of the people around him, a creative will, and a strong will to power. Zarathustra suggests that no overman has yet existed, but that we must try to breed one. As a race, we are only justified by the exceptional people among us. The overman is meant to be the solution to nihilism, the meaning we should give to our lives.
Nihilism
Essentially, nihilism means the belief in nothing. Nietzsche characterized late nineteenth century Europe as nihilistic, and would probably consider the late twentieth century even more so. He generalizes that we no longer believe that God gives meaning and purpose to our lives, but we have found nothing to replace God. As such, we see our lives as essentially meaningless, and lack the will to create or to become anything new. Nietzsche worried that without a purpose we would slide deeper and deeper into a dream world of mediocrity and comfort. He also rightly foresaw that nihilism might lead to a rabid nationalism that would cause horrific wars.
Eternal Recurrence
The doctrine that all events will be repeated over and over again for all eternity. Zarathustra outlines his vision of the eternal recurrence in Part III: If the past stretches back infinitely, then anything that could have happened must have happened already at some time in the past. By that logic, this very instant must have occurred at some time in the past. And similarly, if the future is infinite, everything—including this moment—must recur again sometime in the future. Walter Kaufmann reads this as a scientific hypothesis that is mistaken. Gilles Deleuze reads this as a fundamental expression of the fact that the universe is in a constant state of change and becoming, and that there is no moment of fixity, or being. Nietzsche would probably agree with Deleuze. The overman can look at his past and himself as something entirely willed by himself, and be delighted by the thought that this process (which includes changes) will recur forever.
Dance
Nietzsche often uses dancing as a metaphor for a lightness of spirit. Those who are too serious, and too bogged down by absolutes, such as God, truth, or morality, will be unable to dance. An overman, or a free spirit, who has freed himself from these absolutes will not be weighed down by any seriousness, and will be able to dance. Dancing also metaphorically suggests a kind of mental flexibility and agility that allows a creative spirit to think freely and for himself.
Will to Power
Nietzsche calls the fundamental force that drives all life a "will to power," though he might just as well call it an instinct for freedom. It is the drive to be as free from constraints as possible and to command the wills of others as much as possible. A refined will to power also learns to command and obey itself. The constant struggle for power and overcoming between wills means that nothing in the universe can remain fixed in place for long. Thus, all the universe is in flux.
Overcoming
The words "overcoming" and "overman" are only two of a number of "over-" words that appear throughout
Nausea
In
Evil
This word is often given a meaning contrary to what we normally take it to mean. Something is "evil" only within the context of a given morality. In particular, anything that challenges or tries to destroy a morality is considered "evil" by that morality. Thus, for Zarathustra, "evil" is quite often good. It means doing away with older moralities in favor of something new. He often associates evil with freedom of spirit, and claims that it is essential to creating the higher man.
Laughter
Like dancing, laughter is a common characteristic of the overman. Nietzsche considers laughter to be the activity of someone looking down on someone or something else. As such, it denotes superiority. The overman has risen above everything and everybody, so there is nothing, including himself, that he does not laugh at.
Pity
One of Nietzsche's, and Zarathustra's, pet peeves. A person who shows pity is displaying a perverse and inappropriate amount of interest in the suffering of others. Furthermore, pity harms the person who is suffering, as it makes the sufferer feel pitiful and shamed.