You're talking to a new client. You need him to sign a contract before you can work with him. You hand him the contract and you say this.
Skim over it and let me know if you have any questions.
To "skim" something means to read it very quickly and incompletely. For example, if you "skim" a newspaper, you might read the headlines and a few sentences from some of the articles.
To "look over" something means to look at something to see if it's OK. In other words, it means to "check" something. For example:
I can look over your homework if you want.
In the example above, the speaker combines "look over" with "skim" to make the phrase "skim over". This means to look over the contract quickly.
"Let me know" means "tell me". But "let me know" is a more polite and friendly expression. It's very common to hear in an English-speaking workplace:
"Let me know if you have any questions" is a common way to politely offer to answer someone's questions about something. It's also a good way to end a business email or telephone call when you've given someone information and don't need to ask them for anything. For example:
Attached is a summary of our costs for this month. Let me know if you have any questions.
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