After completing the conversation with Paarthurnax in High Hrothgar, the quests “Discerning the Transmundane” and “Elder Knowledge” become available.
You can actually start this quest as a sub-level 15 character, but you’ll need to be level 15 by the time you return to speak to Septimus Signus.
The races that you must kill include Orsimer (orc), Falmer, Dunmer (dark elf), Bosmer (wood elf), and Altmer (high elf). You can find all but the Altmer in Liar’s Retreat, which is located to the southwest of Solitude. The closest Altmer can then be found in a trap pit in the Halted Stream Camp, which is just northwest of the Whitewatch tower.
Do not read the Oghma Infinium. You can accept or decline the daedra’s offer here—it makes no difference on the bearing of the story itself.
If you own a home that has a bookshelf, fast-travel there instead.
The Path of Might - Grants a +5 level bonus to Heavy Armor, One-Handed, Smithing, Two-Handed, Archery, and Block skills. The Path of Shadow - Grants a +5 level bonus to Light Armor, Speech, Pickpocket, Alchemy, Sneak, and Lockpicking skills. The Path of Magic - Grants a +5 level bonus to Destruction, Restoration, Conjuration, Illusion, Alteration, and Enchanting skills.
Be sure to quick-save intermittently so that you don’t have to redo all of your progress if you accidentally break the glitch.