Learn Hardcore Japanese: ame ga huru kara, kasa wo motte ikimasu. - Since it will rain, I will take an umbrella.

Here, 雨が降る is simply stating that “rain falls” – が marks the grammatical subject of the verb 降る. If you said 雨は降る, you’d be using は to set “rain” as the topic, implying contrast or presupposing known information. In everyday weather reports or explanations of cause-and-effect, が is more natural for “it is raining.”

What function does から serve in this sentence?

から here means “because” and connects two clauses:
1) 雨が降る (“it rains”) – the cause
2) 傘を持っていきます (“I’ll take an umbrella”) – the effect
Putting から after the cause clause explains the reason for the action in the second clause.

Why is 降る in the plain dictionary form before から? Could I say 降りますから instead?

The original sentence mixes plain (降る) and polite (持っていきます) styles, which Japanese speakers sometimes do in conversation. If you want to keep everything polite, you can absolutely say:
降りますから、傘を持っていきます。
Doing so makes both clauses uniformly polite.

Why is 傘 followed by the particle を?

持つ (“to hold, carry”) is a transitive verb—it requires a direct object. The particle を marks 傘 as the object being carried. In English: “I will take an umbrella,” where “umbrella” is what you take.

What does 持っていきます literally mean?

This is a compound of the て-form of 持つ plus いく:
• 持って – “holding/carrying”
• いきます (行きます) – “to go”
So 持っていきます literally means “go carrying [it] away,” i.e. “take [something] with me.”

Why use 持っていきます instead of simply 持ちます?

• 持ちます = “I hold/carry” (neutral)
• 持っていきます = “I’ll take (it) with me (to another place).”
Here you want to express that you’ll bring the umbrella along when you go (e.g. leaving home). 持っていきます conveys the idea of moving something from here to there.

What nuance does the ていく/てくる construction add?

• ていく emphasises movement away from the current location or standpoint.
• てくる emphasises movement toward the current location or standpoint.
In 持っていきます, you’re focusing on going somewhere (perhaps outside) while carrying the umbrella.

Could I reverse the order to say 傘を持っていきますから、雨が降る?

Technically you can switch clauses, but Japanese typically places the reason (cause) before the conclusion (effect). Reversing it sounds awkward or overly casual:
“傘を持っていきますから、雨が降る。”
It isn’t ungrammatical, but native speakers prefer 雨が降るから、傘を持っていきます for clarity and natural flow.