There is a linearly constant amount of 'experience' required for each level.

Level 81 is the maximum level in Skyrim without making any skill Legendary It is possible to repeatedly make a skill legendary or to make multiple skills legendary, this allows you to (slowly) unlock all perk points. You can continue to level up and earn extra skill perks.Difficulty increase, since the enemies don't have their skills reduced.Be warned: You lose all the benefits of having a higher skill level! The advantages of making skills legendary are: This resets the skill to 15, gives all perk points invested in that specific tree back. If you have a skill at 100 you can make it 'Legendary'. Since patch 1.9 there is no maximum level anymore.