Learn Russian: У тебя есть билет в театр?

In Russian, possession is usually expressed by saying 'At someone there is something' rather than 'Someone has something.' Here, У means 'at', тебя is the genitive form of ты (informal you), and есть means 'is' or 'exists'. So literally, you are asking 'At you there is a ticket?'

Why use тебя and not ты or вас here?

The preposition У always requires the noun or pronoun following it to be in the genitive case. Therefore, the dictionary form ты changes to тебя. If you were speaking formally or to multiple people, you would use вас (the genitive of вы), making it У вас есть.

Is билет the object of the sentence since it is the thing being owned?

Actually, no! Because of the 'At you there is...' structure, the thing being owned is the grammatical subject of the sentence. билет (ticket) is in the nominative case, which is the basic dictionary form used for subjects.

Why is it в театр? Doesn't в usually mean 'in'?