Learn Polish: Nie ma już nadziei. - There is no hope left.

The phrase nie ma (there is not) always requires the noun that follows to take the genitive case. Because of this, the feminine noun nadzieja (hope) takes the genitive ending -i.

Doesn't już usually mean "already"? How does it mean "left" here?

While już does mean "already" in affirmative sentences, pairing it with a negated verb creates the structure nie ... już. This combination translates to "no longer", "not anymore", or in this context, "no ... left".

Why is there no Polish word for "there" at the beginning of the sentence?

English uses "there" as a dummy subject in phrases like "there is" or "there are". Polish drops dummy subjects entirely. The impersonal phrase nie ma is completely sufficient on its own to express "there is no".

Why does the genitive form of nadzieja end in -i instead of -y?

Feminine nouns ending in -ja are treated as having a soft stem in Polish. Because of this softening, they take the -i ending in the genitive singular, resulting in nadziei rather than taking the hard-stem -y ending.