Let me (do something)

When you see or hear the words "Let me...", you may think that the speaker is asking for permission, but that's not true. This phrase is used in both casual and formal situations to announce what you're going to do:

Let me give you a few examples.

This is more confident-sounding than "I'd like to ___". It's more polite than "I'm going to ___."

take (someone) around

Use this phrase to talk about giving someone a tour. You can give someone a tour of a city:

I had some friends come to visit from out of town, so I took them around and showed them the sights.

Or a company, school, etc:

Ana, why don't you take him around and show him where everything is?

The phrase "take ___ around" is more casual than "give ___ a tour".

introduce (someone) to (someone)

When you "introduce" a person, you explain who they are.

To talk about introducing people, we use the form "Introduce (A) to (B)". It's a little unclear in this situation which person you're talking about, and which person you're talking to. For example:

Have I introduced you to Monica?

This means "Have I explained to you who Monica is?" but it also means "Have I explained who you are to Monica?"

We also use the phrase "Introduce ___ to each other."

I think I'm the one who introduced Bill and Ali to each other.

everyone

We sometimes use the word "everyone" to talk about everyone in a specific group. For example, if a friend comes to your dinner party, ask:

Thu, have you met everyone?

It means "Have you met everyone at this party?"