Hello. I would be very grateful if you helped me with a few sentences.

1) Which part of the book did you like the most? (Did I use "the most" correctly?)
2) Anlyze US involvement in global affairs. (I didn't use THE before US involvement. Am I right?)
3) Speak on the prospects for Turkey's integration into the EU. (I'm not sure whether it's FOR, maybe, OF?)
Thank you very much.

1 and 2 are correct.

3. For is o.k., but of is better.

Thank you, dear Ms.Sue.

You are very welcome, Ilma.

Hello! I'd be happy to help you with your sentences.

1) "Which part of the book did you like the most?" - Yes, you have used "the most" correctly in this sentence. "The most" is used to refer to the highest degree or level of liking, and it is appropriate in this context.

2) "Analyze US involvement in global affairs." - You are correct in not using "the" before "US involvement" in this sentence. When we talk about general or abstract ideas, we often omit the definite article "the." In this case, you are referring to the broader idea of US involvement in global affairs, rather than a specific instance of it.

3) "Speak on the prospects for Turkey's integration into the EU." - You used "for" correctly in this sentence. "For" is appropriate when discussing the prospects or possibilities that exist regarding a certain topic. In this case, you are discussing the possibilities for Turkey's integration into the EU.

I hope that helps! Let me know if you have any more questions.