After I make an effort to visit the PHP script at http://localhost/project/admin, I anticipate seeing the script leads to my internet browser.

Rather, I visit a dialog box for installing the file using the message below:

You've selected to spread out <filename>, the industry: application/x-httpd-php from: http://localhost
What should Opera use this file? Open with... &bullet Save... &bullet etc.

Any idea what's going on?

It sounds somewhat incorrect Content-type header has been sent. This header sets the mime-type for that data the browser receives and, when the browser does not possess a handler to render that mime-type, it'll request to spread outOrconserve the file rather.

I'd begin by checking your PHP apply for a header() statement along with a mis-typed content-type.

PHP isn't properly placed on the server or Apache isn't using mod_php

Within the situation of the happening in IIS. I'd state that the mimetype isn't setup properly which the server does not understand how to handle the extension ".php"