Which of the preposition is most suitable to use;
I) I will have finished my thesis by March.
II) I will have finished my thesis until March.
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Generally, you can't finish something until a specific time, since finishing is a sudden action and until emphasises duration; in other words, if something happens until a particular time, it continues and then stops at that time as in
The ticket is valid until March.
You have to stay here until March.
By, on the other hand, means before or not later than a particular time as in
The documents need to be ready by next Friday.
You need to finish your paper by Tuesday.
In your case then, I'd definitely go with by and not until.
'by' sets the deadline. This means the work should be finished before that time. Here, in this case, the thesis' deadline is the month of March.
'until/till' talks about something that is continued from one point to another. Say - "I will wait for you till 2 o'clock". This means from this point of time to 2 o'clock'.
She's sick. She needs to be in bed till 10 o'clock.
This means from one point of time to 10 o'clock, she should be in her bed.
She's sick. She needs to be in bed by 10 o'clock.
sets the deadline that no matter where she is, she has to be in her bed before clock strikes 10.
In your example, '..by March...' is the choice.