być — the Polish verb 'to be'

The present tense

Six forms, all irregular, all worth memorising as a block. Note that the endings -em, -eś, -eśmy, -eście are the same ones that mark the past tense of every other Polish verb, so learning them here pays twice.

Polish does not drop it

In Russian and Ukrainian the present tense of 'to be' is normally left out: «Я студент». Polish keeps it. 'Ja student' is not a clipped sentence in Polish, it is not a sentence at all. Say 'Jestem studentem'.

The pronoun, on the other hand, usually goes. The verb ending already says who is speaking, so 'Jestem z Ukrainy' is the normal way to say it; adding 'ja' puts a stress on it, as if answering someone who thought otherwise.

What comes after być: the instrumental

When you say what somebody is — a profession, a role, a nationality as a noun — the noun goes into the instrumental case, not the dictionary form. student becomes studentem, lekarka becomes lekarką. This is the single most common beginner error in Polish, and it is completely regular: -em for masculine and neuter, -ą for feminine.

Adjectives alone are different. 'I am tired' describes a state, not an identity, and takes the plain form: Jestem zmęczony. The rule of thumb: a noun after być goes instrumental, an adjective after być does not.

to jest — pointing at things

There is one place where the noun stays in its dictionary form: after 'to jest', which points at something rather than identifying a person. 'To jest student' is 'this is a student' — and here student does not change.