My 4th junior high english class: BY THE TIME -TILL

By (+ a time) = not later than:

I sent the letter to them today, so they should receive it by Monday.
(= on or before Monday, not later than Monday)
We’d better hurry. We have to be home by 5 o’clock.
(= at or before 5 o’clock, not later than 5 o’clock)
Where’s Sarah? She should be here by now.
(= now or before now – so she should have already arrived)

‘Shall we go now?’ ‘No, let’s wait until (or till) it stops raining.
I couldn’t get up this morning.
I stayed in bed until half past ten./ I didn’t get up until half past ten.

Compare until and by:
Something continues until a time in the future:

Something happens by a time in the future:

David will be back by Monday.
(so he’ll be back not later than Monday)
I’ll have finished my work by 11.30.
(= I’ll finish my work not later than 11.30.)

It’s too late to go to the bank now. By the time we get there, it will be closed.
(= the bank will close between now and the time we get there)
(from a postcard) Our holiday ends tomorrow. So by the time you receive this postcard. I’ll be back home.
(= I will arrive home between tomorrow and the time you receive this postcard)
Hurry up! By the time we get to the cinema, the film will already have started.

You can say ‘by the time something happened’ (for the past):

Karen’s car broke down on the way to the party last night. By the time she arrived, most of the other guests had left.
(= it took her a long time to get to the party and most of the guests left during this timei
I had a lot of work to do yesterday evening. I was very tired by the time I finished.
(= it took me a long time to do the work, and I became more and more tired during this time)
We went to the cinema last night. It took us a long time to find somewhere to park the car. By the time we got to the cinema, the film had already started.

Also by then or by that time:

Karen finally arrived at the party at midnight, but by then (or by that time), most of the guests had left.