Our contractor just installed new lights with a dimmer switch. When the lights are on, the switch gets too hot to hold your hand on. Our contractor said this normal. Is a hot dimmer switch normal? If not what is the problem and how do you correct it?

It is completely true that dimmers get hot. "Too hot to hold you hand on" is a subjective term.

What is the dimmer rated? 600 watts or 1000 watts?
How many watts is it controlling?

No dimmer likes to be very near it's maximum capacity.

There are two dimmers in each box. One has 9 lights @ 65 watts each for 520 watts. I don't know the wattage of the dimmer. The other dimmer has 5 ea. 30 inch strip lights with four halogen bulb in each strip. I don't know the wattage of these lights, but with halogen lights I think it would be high.

OK then. The two dimmers in a box thing presents a problem. When you gang dimmers together you must derate them. Typically by 100 watts per added gang.
So two 600 watt dimmers next to each other would derate them to 500 watts each.
If these are standard 600 watt dimmers they are not good to use for 520 watts. They will certainly work, but they will get much hotter than they are supposed to.

I think we have our answer.

Was this a builder who put them in, or a real electrical contractor?

The remodeling contractor installed the dimmer switches.
I will find out the rating of the dimmers switches and calculator the wattage we actually have.

Thanks for your help!

Usually if the dimmers are installed in the middle or the end of a box, you have to "break off" part of the heat sink and derate them for two reasons. Less surface for the heat sink and multiple dimmers.

A metal face plate helps with some dimmers.