Learn Hardcore Russian: Я уже купил билеты на поезд.

Уже means “already.” It signals that the action (buying tickets) is completed by now or earlier than expected. In Russian it often comes before the main verb to stress that the event has taken place.

Why is купил in the past tense perfective, and what does that tell me?

Купил is the past tense form of the perfective verb купить (“to buy [completely]”). Perfective aspect in Russian indicates a completed action. Here, it fits naturally with уже, because you’re stating the purchase is finished.

Why is купил masculine? What would a woman say?

Past-tense Russian verbs agree in gender and number. Купил is masculine singular. A female speaker would use купила; a plural subject (they) would use купили.

What case is билеты, and why is it used here?

Билеты is the accusative plural of билет (“ticket”). Купить takes a direct object, which goes into the accusative. For inanimate masculine nouns in plural, the accusative form is identical to the nominative.

Why does на govern the accusative in на поезд?