If you find a page that you want to download, select "File", then "Save as..". Select a location to save to, and select the "Web Archive" format. You can then access the page from your hard drive, even if the internet is down.
"The" internet is far to large, and changes far too much for it to be downloaded onto any one machine.
In fact, in 2002, the size of the internet was judged to be 532,897 terabytes.