Learn Farsi: این چتر برادر من نیست. - This is not my brother's umbrella.

Farsi uses the Ezafe particle, which is an "-e" sound, to link nouns together for possession. Instead of using an apostrophe-s like in English, Farsi builds a chain meaning "umbrella of brother of me". So, chatr (umbrella) takes an Ezafe to become chatr-e, and barādar (brother) takes an Ezafe to become barādar-e, giving us the chain chatr-e barādar-e man.

I don't see the Ezafe "-e" written anywhere in چتر برادر من. Why is that?

In the Farsi alphabet, short vowels like "a", "e", and "o" are usually not written out. As a learner, you just have to know that when nouns are linked together to show possession, you must pronounce the invisible "-e" between them. You read it as chatr-e barādar-e man, even though the written letters only spell "chatr barādar man".

Why is نیست (is not) at the very end of the sentence?

In Farsi, the verb almost always goes at the very end of the sentence. While English says "This is not my brother's umbrella", Farsi builds the sentence as "This [Subject] my brother's umbrella [Complement] is not [Verb]".

How does نیست relate to the normal word for "is"?

The positive word for "is" is ast. To make it negative ("is not"), Farsi uses a special combined word: nist. You can think of it as combining a negative "n-" sound with ast, which transforms into the single word nist.