Learn Hardcore Japanese: kyuukou ni noru tame ni, eki de kippu wo kaimasita. - I bought a ticket at the station to ride the express train.

In Japanese, when you “ride” or “board” something (like a train, bus, ship, etc.), you mark that thing with に. So 急行に乗る literally means “to board the express train,” with 急行 being the thing you get on.

Why is the verb 乗る in dictionary form before ために, and why does 急行に乗るために have two にs in a row?

乗る is in the plain (dictionary) form because ために attaches to the plain form of a verb to express purpose (“in order to …”).
The first に belongs to 乗る (marking what you board), and the second に is part of ために (the fixed expression “for the purpose of”). They serve different roles.

What does ために mean and how does it work here?

ために means “for the purpose of” or “in order to.” It connects a reason/purpose clause to a main clause. Structure:
[Verb-dictionary-form] + ために, [main clause]
Here: 急行に乗るために、駅で切符を買いました。
“In order to board the express train, I bought a ticket at the station.”

Could I use ように instead of ために to express purpose?

Not in this case.

ために is used for deliberate, volitional actions under your control (“I did X in order to do Y”).
ように is used for wishes, indirect commands, or events you cannot directly control (“so that…”).
Since buying a ticket is a deliberate action to achieve boarding, ために is correct.

Why is 駅で marked with で rather than に?

で marks the location where an action takes place. Buying a ticket is an action, so it happens at the station—駅で買いました. If you used に, it would sound like “towards the station” or a time marker (“at [a point in] the station”), which doesn’t fit here.

Why is the verb 買いました in the past tense? Could it be present instead?

The speaker is narrating that the ticket purchase has already been completed. If you said 買います (present/future), you’d imply “I will buy a ticket in order to ride the express,” which changes the timing. Past tense (買いました) matches “I did that, and now I’ve boarded (or am ready to board).”

Is the comma after ために necessary?

No, it’s optional. Japanese often uses commas to clarify or separate clauses, especially in writing. You can write 急行に乗るために駅で切符を買いました。 without a comma, and it’s still perfectly correct.

Can I reorder the sentence, for example: 駅で切符を買うために急行に乗ります?

Grammatically, you could shift elements around, but the purpose clause (…ために) typically comes before the main action. Also, your example changes meaning to “I will board the express in order to buy a ticket at the station,” which reverses cause and effect. To keep the original purpose (“buy ticket so I can ride”), keep 急行に乗るために、駅で切符を買いました。 in that order.