English modal verbs

Emily - Andrew, I'm having a few problems with modal verbs.
Teacher - Ah, don't worry Emily, they're a bit like a jigsaw puzzle it's simply a cuestion of time you can do anything if you put your mind to it.

E - Can you help me then?
T - No problems. We'll start with one of the most common verbs. The verb can expresses ability o permission:
I can play tennis or
Can I go with you?

E - And what about may and could?
T - Use may or could for permission:
May I come in? or
Could I go with you?

E - Right. Are in may and could also uses for possibility?
T - Yes. That's right:
It may rain. But for remote possibility you could use might:
It might also snow.

E - What do I use for obligation?
T - You must use must or have to:
I must catch my train or
I have to catch my train.

E - Right. And what about should?
T - You should use should for giving advice or recommendations:
You should drink more water and
You should try de new Chinese restaurant.

E - Will is for the future, ins't it?
T - Yes, will is the best form of the future in all cases. Even for the first person:
I will see you tomorrow.

E - And what about shall?
T - Shall is for making suggestions and offering help:
Shall we have a drink? 
Shall I carry your bag?

E - Oh, thank you Andrew. This is a very interesting lesson. You are a terrific teacher. I'm going to make a frame for this lesson to keep forever. Can I also have a photo of you to put in my frame?
T - Let me get the frame for you. Then I can dedicate it to you: To my best student with love for men.

E - Oh, thank you Andrew.