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In D&D 5E Wizards get an additional two spells per level to add to their spellbook:
Each time you gain a wizard level, you can add two wizard spells of your choice to your spellbook.
If a Wizard has a handful of Scrolls and another Wizard's spellbook they have found while adventuring, can they attempt to scribe them all (assuming they are of the necessary spell level and have the time and money to do so), or are they limited to 2 new spells per level?
Note the full wording1 of the Learning Spells of 1st Level and Higher section (emphasis mine):
Each time you gain a wizard level, you can add two wizard spells of your choice to your spellbook for free. Each of these spells must be of a level for which you have spell slots, as shown on the Wizard table. On your adventures, you might find other spells that you can add to your spellbook (see the “Your Spellbook” sidebar).
There is a clear distinction here. Whenever you gain a level, you get two free spells. Separately, you might add other spells to your spellbook, as detailed in the spellbook sidebar. These are two separate methods of getting additional spells for your spellbook.
So if you have scrolls or another spellbook, you can copy any of those spells following the costly copying method, independently from the free spells obtained at level up.
1. Apparently some older versions of the PHB did not have "for free" at the end of the first sentence of the quote. It seems to have been added silently (without being noted in the errata docs), according to Someone_Evil.
The section “Learning Spells of 1st Level and Higher” states:
Each time you gain a wizard level, you can add two wizard spells of your choice to your spellbook for free.
So when you level, you get two spells for free.
This section continues:
When you find a wizard spell of 1st level or higher, you can add it to your spellbook if it is of a spell level you can prepare and if you can spare the time to decipher and copy it.
For each level of the spell, the process takes 2 hours and costs 50 gp. The cost represents material components you expend as you experiment with the spell to master it, as well as the fine inks you need to record it. Once you have spent this time and money, you can prepare the spell just like your other spells.
Learning spells this way is not free. This is a distinct class feature from learning spells by leveling up, so the two do not restrict each other in any way.
