Galea, Kindler of Hope — ruling 1

You can look at the top card of your library whenever you want (with one restriction; see below), even if you don't have priority. This action doesn't use the stack. Knowing what that card is becomes part of the information you have access to, just like you can look at the cards in your hand.

Galea, Kindler of Hope — ruling 2

If the top card of your library changes while you're casting a spell, playing a land, or activating an ability, you can't look at the new top card until you finish doing so. This means that if you cast a spell from the top of your library, you can't look at the next card until you're done paying for that spell.

Galea, Kindler of Hope — ruling 3

Galea, Kindler of Hope doesn't change when you can cast Aura and Equipment spells. Normally, this means during your main phase when the stack is empty, although flash may change this.

Galea, Kindler of Hope — ruling 4

You'll still pay all costs for the spell, including additional costs. You may also pay alternative costs if any are available.

Galea, Kindler of Hope : règles, fonctionnement et interactions (MTG)

Galea, Kindler of Hope is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Vigilance You may look at the top card of your library any time. You may cast Aura and Equipment spells from the top of your library. When you cast an Equipment spell this way, it gains "When this Equipment enters, attach it to target creature you control."

How it works : Galea, Kindler of Hope

Original English text — Wizards of the Coast / Scryfall

#1July 23, 2021· Wizards of the Coast
You can look at the top card of your library whenever you want (with one restriction; see below), even if you don't have priority. This action doesn't use the stack. Knowing what that card is becomes part of the information you have access to, just like you can look at the cards in your hand.
No other card is named in this ruling.
#2July 23, 2021· Wizards of the Coast
If the top card of your library changes while you're casting a spell, playing a land, or activating an ability, you can't look at the new top card until you finish doing so. This means that if you cast a spell from the top of your library, you can't look at the next card until you're done paying for that spell.
No other card is named in this ruling.
#3July 23, 2021· Wizards of the Coast
Galea, Kindler of Hope doesn't change when you can cast Aura and Equipment spells. Normally, this means during your main phase when the stack is empty, although flash may change this.
No other card is named in this ruling.
#4July 23, 2021· Wizards of the Coast
You'll still pay all costs for the spell, including additional costs. You may also pay alternative costs if any are available.
No other card is named in this ruling.