Learn Russian: Мой брат живёт здесь.

The verb жить (to live) is irregular. In the present tense, its stem changes by adding a в. Instead of adding endings to жи-, you add them to жив-. Since брат is "he" (third-person singular), we add the ending -ёт to get живёт.

Why is the ending of живёт spelled with ё instead of е?

In Russian present-tense verbs, if the spoken emphasis falls on an -ет ending, it changes to an -ёт. Since the stress in this word is on the last syllable, it gets the two dots. As a helpful bonus, the letter ё is always stressed in Russian!

Why do we use Мой instead of Моя?

Russian words like "my" must match the gender of the noun they describe. Because брат (brother) is a masculine noun, we use the masculine form Мой. If you were talking about a sister (сестра), you would use the feminine form Моя.

Could I use тут instead of здесь in this sentence?

Yes, absolutely! Both здесь and тут mean "here". The word здесь is a bit more standard for writing and neutral speech, while тут is very common in casual, everyday conversation. Saying Мой брат живёт тут means exactly the same thing.