By Monday morning. vs On Monday morning.

[i]- May I encourage you to have chapter 5 read by Monday morning.
VS.

  • May I encourage you to have chapter 5 read on Monday.[/i]

Does the first sentece mean we should read it on Monday?
OR
we should finished reading it before monday?

No, it should be finished before Monday morning. It is an example of “elliptical” usage.
What the speaker is saying is “May I encourage you to have chapter 5 read by (the time you get here on) Monday morning.”