Am I to understand ?? what's this ?
Am I to understand you're still hanging
around with Dr. Emmett Brown, McFly?

I don't know this grammartical phrase
"Am I to understand that S+V" ?
What does it mean ?

Question

Am I to understand ?? what's this ?
Am I to understand you're still hanging
around with Dr. Emmett Brown, McFly?

I don't know this grammartical phrase 
"Am I to understand that S+V" ?
What does it mean ?

Answer

Am I to understand = let me get this straight = let me make sure I understand = I want to be clear, what you are saying is ...

Answer

"So, what you're saying is _______"
"Am I to understand ______?" just sounds more formal. It sounds like what a teacher would say to you when you're in trouble. I think I can go into more detail if you'd like, but that's the gist of it.

Answer

It's an expressive way to say "As far as I understand..."

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