Learn Polish: W centrum jest stare muzeum. - In the centre there is an old museum.

The preposition w (in) requires the Locative case here, which usually changes the ending of a noun. However, centrum is a special loanword ending in -um. In Polish, all nouns ending in -um stay exactly the same in all singular cases.

How do you say 'there is' in Polish? I only see the word jest (is) here.

Polish doesn't have a direct equivalent to the English phrases 'there is' or 'there are'. To express that something exists somewhere, you simply use the verb być (to be) — in this case, jest (is) — and often place it before the subject.

Why does the adjective stare end in -e?

Stare (old) describes muzeum. Because muzeum is a neuter noun (almost all nouns ending in -um are neuter), the adjective must take the neuter Nominative ending, which is -e.

Since muzeum also ends in -um, does it follow the same no-change rule as centrum?

Yes! Just like centrum, the word muzeum won't change its form anywhere in the singular. For example, if you wanted to say 'in the old museum', it would be w starym muzeum (notice that the adjective changes to starym, but muzeum stays exactly the same).