How many spells known per level does a level 3 wizard get, and where do you find that info in the PHB?
On the chart in the wizard chapter, there is only spell slots, not spells known.
Welcome, please reread the game rules rather than just asking questions that amount to 'read the rules for me'. That being said, I'll still answer it.
@TiwazTyrsfist nobody ever accused D&D's wizard magic of being terribly easy to understand, nor WotC's expression of it terribly easy to interpret. The rules for which spells a wizard has in their spellbook, knows (prepares), has on their "list", &c. are spread across hundreds of pages and only really make sense to someone who already knows the deal. Answer or don't, but I don't think OP needs that ^^ kind of welcome.
PHB p. 114, under the Preparing and Casting Spells heading. 2nd paragraph, 2nd sentence
...To do so, choose a number of wizard spells from your spellbook equal to your Intelligence modifier + your wizard level (minimum of one spell)...
If you're asking about how many spells they should have in their spell book, also on p.114, Under the heading Spellbook at the top of the page,
...You have a spellbook containing 6 first level wizard spells...
and at the bottom of the page under Learning Spells of 1st level and Higher,
Each time you gain a wizard level, you can add two wizard spells of your choice to your spellbook.
So, assuming you have a 16 Int, a third level Wizard can prepare 6 spells (3 int mod + 3 level), and your spellbook should contain 10 spells, probably 8 1st level and 2 2nd level.
Seems like the OP wants to know how many spells they should have in their spellbook, not how many they can memorize (though I'll admit it's hard to tell).