[RPG] Question regarding spellcraft: Learn a spell

Yes, but only 1st-level spells

PurpleVermont has already argued why such a multiclass could only write down spells of a level they could cast as a Wizard (so actually up to 2nd level, if they take Wizard 3). I disagree with Vermont's argument that stolen spells could not be transcribed at all, however.

The rules don't clearly state that you have to have seen a spell written down to be able to transcribe it, that's a matter of interpretation--and I disagree with the interpretation:

Copying a spell into your spellbook involves reproducing the basic form of the spell, then deciphering the unique system of notation used by the wizard who wrote it. You must practice the spell until you understand the sounds or gestures required, then transcribe it into your spellbook using your own notation.

The fact that different wizards use different notation implies that the written form of the spell is not an inherent part of the magic, merely an aide-memoire. And the requirement to practice the spell until you understand its V/S requirements -- precisely the thing which the Arcane Trickster can instantly intuit -- strongly suggests that this is the most important part of "learning" a spell, and the rest is merely paperwork that your first-level Wizard training would absolutely prepare you for.

There are other arcane spellcasting classes that use spellbooks, like the magus. The alchemist has a “formula book” that works mostly the same way, and the witch has a familiar that functions like a spellbook for her.

In all of these cases, however, learning from scrolls is reserved for a class with very wizard-like spellcasting, that is, they must prepare exactly which and how many of each spell they know in advance.

As you note, the divine spellcasters who, like the wizard, prepare spells ahead of time don’t need to bother with spellbooks at all. Clerics, druids, and similar divine spellcasters can pray for any spell on their list, even one they have never seen before. In effect, you can think of the gods they pray to as being giant spellbooks that already have every spell available ready to go.

On the other side of the coin, we have spellcasters that do not have to prepare their spells ahead of time. The sorcerer is the quintessential example, but others exist, including some like the oracle that are divine (as you note). These “spontaneous” classes do not keep a spellbook or similar, and they cannot take advantage of the rules for copying a scroll into a spellbook. Scrolls, for them, can only be used as a scroll, not used to learn a spell. To learn a spell, they need the vastly more expensive page of spell knowledge, or the even more expensive ring of spell knowledge (which then does allow them limited ability to learn spells from scrolls and other sources).

The advantage to spontaneous spellcasters is that they are free to use these spells in any combination they like, up to their spells per day limit, where spellcasters that prepare have to choose exactly how many of each spell they want. However, generally speaking, the advantage of having access to so many spells is vastly superior, so clerics and druids and wizards are generally better than oracles and sorcerers and the like.