This lesson will be about ～て（も）いい. This is an essential part of many sentences for asking and giving permission to someone to do something.
～て(も)いい is used to ask for permission. As speech level changes this phrase, this is a good time to review these processes. Remember that も makes the sentence more indirect, thus making it more polite. The particle adds the meaning of "even if I".
The addition of the particle も emphasizes the sense of "if you do X, that's OK", and it is often used to give a softening effect. This is why it is usually seen when asking questions as to be more polite.
Mom! Can I see a movie tonight?
Excuse me, is it alright if I smoke?
Mm, is it fine for me to sit by you?
May I open the box?
Because there is a lot of them, it's OK if you don't proofread them all.
May I come in?
President Kuroda, may we sit down here?
May he sit down here?
9. 社長、この本をお借りしてもよろしいでしょうか。(Humble Speech)
President, may I borrow this book?
May I have you fill this out here?
Sentence Note: In honorifics, it is important to lessen the effect of pushing a request on someone. So,～てよろしい is seen here asking for permission to make a request to the listener.
許可 Not 依頼
～ていい asks for permission, not request. In any case, the listener could still say no. If you were to use ～ていい with 借りる (to borrow), the listener is the person you're seeking permission to borrow. The listener is not the person lending you the money （貸す人ではない!）. We can surmise that the only people that would say something like お金を貸してください are bank deposit salesmen or loan sharks, but friends wouldn't use it among each other.
11a. 先生に〇を習ってもいいですか？ X
Sensei, may you teach me 〇?
12a. 10万円を借りてもよろしいですか。 X
Could I please have you lend me 100 thousand yen?
Is it alright if I borrow from a friend?
14. 細かいのがないので、ちょっと10円｛借りてもいい X・貸してくれない｝？
I don't have small change, so could I borrow 10 yen?
Sentence Note: Here, the difference between the English "borrow" and Japanese 借りる is quite clear. It is not that 借りていい itself is faulty, but it's wrong for the sentence the English speaker tried to convey.
Another equivalent phrase ～[て・で]結構. It shows that something is fine but may not be entirely satisfactory.
Particle Note: As you should know by now で＋も results in the particle でも.