micro controller

I am very new to micro controllers. I have just one quick question. if I program a micro controller, can i remove it from the programmer and have it run another project by itself.

Yes, you can. The programmer is used to store a program into the Flash memory inside the microcontroller. The program will remain in that memory until it is deliberately erased. So, after you remove the chip from the programmer, it will continue to run the program that you put into it.