Cannot smooth without trouble on my mesh I'm working on my mesh which looks like this : 


As you can see the surface is not smoothed. Then I apply the smooth option and it gives me this result : 


It is the third times I start again this mesh... I cannot understand how to apply the boolean modifier without getting in troubles.

Thank you for your help.
Thank you for your helps, it is solved.

What I have done is : 

I have added a subdivision modifier


Then I have smoothed the surface. At this time, problems were still present on my mesh. 


Finally, I have activated auto-smooth option 


What I get is alright : 


Thank you for your help guys !