I'm a new player and I have Xzar in my party.
I'm trying to learn my first spells.
Some spells appear in green and have the "write spell" button, but others don't.

What happens here?

Xzar is a necromancer, a specialised mage. When a mage is specialised they have one or two opposition schools of magic which they cannot learn nor use. The opposition school to necromancy is illusion, so any illusion spells he cannot learn.

As a necromancer, Xzar can't cast illusion spells, if that is what you want him to do.

He also can't learn spells he already knows

Also a mage (with INTelligence below 19) only has a chance to learn a spell. (At 19 intelligence the mage's chance to know a spell is 100%.)

No, at 19 it's only 95%. (Also there's a bonus chance for learning spells from the school of specialization).
Baldur's Gate: Races and Stats - Intelligence.

Hi scientiae! Just an FYI -

The Baldur's Gate CRPGs (loosely) use the AD&D 2nd Edition pen-&-paper rules.

All versions of the hardcover AD&D 2E Player's Handbook (1989, 1995, and 2013) have the same Intelligence table. Within this table, this is the "Chance to Learn Spell" column:

Int 16 = 70%
Int 17 = 75%
Int 18 = 85%
Int 19 = 95%
Int 20 = 96%
Int 21 = 97%
Int 22 = 98%
Int 23 = 99%
Int 24 = 100%
Int 25 = 100%

And the AD&D 2E PHB also says that Specialist Wizards receive a bonus of +15% when learning spells from their school, and a penalty of -15% when learning spells from other schools. (And of course a Specialist can't learn a spell at all if the spell is from an "opposition school".)

So, if I am an Invoker with Intelligence of 18 trying to learn the Fireball spell (my school), then pen-&-paper rules dictate a 100% chance of learning the spell (85% + 15%). (I am not sure how the BG CRPG engine does it.)

Also, I believe Bioware developed the BG CRPGs, and Black Isle published the games.

(Someone correct me if I am wrong on any of this.)


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Thank you. :)