Zarathustra - Zarathustra was a Persian prophet (called "Zoroaster" by the Greeks, and most of the Western world) who lived and preached in the fifth century B.C.E. He was the first philosopher to conceive of a universe that is fundamentally defined by a struggle between good and evil. Nietzsche uses him as his protagonist, since, Nietzsche supposes, the first prophet to preach about good and evil should also be the first to move beyond good and evil. In the book, Zarathustra preaches about the overman who has moved beyond the concepts of good and evil, and has embraced the eternal recurrence. It is unclear whether or not Nietzsche means Zarathustra himself to be an overman, though if this is the case, he only becomes so in the fourth part of the book, when he finally embraces the eternal recurrence.
Overman - 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.
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 Zarathustra. The concept of overcoming is probably the most central, however. Any improvement in a person is made at the expense of what that person used to be. Thus, in order to improve myself, I must learn to overcome myself. In ##Beyond Good and Evil##, Nietzsche speaks of humans as being part creature and part creator, and that our refinement consists in the fact that the creator in us can torture and re-shape the creature in us. The overman is someone who has fully overcome himself so that he can claim to be all creator and in no way a creature: he is fully responsible for everything he is.
Nausea - In Zarathustra, the feeling of nausea, or disgust, is usually associated with contemplating the common people. In particular, Zarathustra has a hard time in part three facing the full consequences of the eternal recurrence, because he is overcome with nausea at the thought that the mediocrity of humanity must recur eternally without change.
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.