i wish to give a submenu to some menu subitem in Joomla 1.7. Example:

[Main menu]
  **First Institute**
  Second Intitute

[First Institute submenu]
First link
Second link
Third link

Around the primary menu i have opened up Intitutes link and under that i have opened up First Institute, which sprang another submenu known as [First Institute submenu] elsewhere around the page. Now after i navigate around the submenu, the very first menu continues to be same and link Bold. How do you start doing that?

You should utilize a 'Split Menu' technique. Here's one example