A Wizard learns two spells for free whenever they level up, and may learn additional spells by copying from spellbooks or scrolls.
For example, if there were two Wizards in the party, I assume they could each learn two different spells and then learn from each other's spellbooks.
Otherwise, the Wizard can either have only those two spells per level or, at the other extreme, all the spells, depending on what DM gives the player acccess to.
Will giving the Wizard a very large number of spells to learn from (for example, by having a high-level friendly mentor who charges no cost for access to their spellbook) cause them to become far more powerful than other PCs? I'm interested only in combat encounters.
Best Answer
A Wizard with hundreds of spells in their spell book cannot cast more than any other Wizard of the same level. Two Wizards of equal level prepare the same number of spells and can cast the same number of spell slots.
The Wizard with the large repertoire has more options and can fine-tune their selections if they know what they are going to face. Most adventurers don't have that much insight into what they are going to face so the advantage may be marginal.
On the other hand, a large repertoire can be a boon if they have the time, resources, and inclination to prepare scrolls ahead of adventures.