Very good histories of the Internet are available on the web site of the Internet Society. They provide such excellent information that it would be superfluous to try to reproduce it here. Note that the Internet and the World Wide Web are not the same thing. See also: who invented the World Wide Web?
See also Hobbes’ Internet Timeline for another excellent history of the Internet which includes later important events, such as the lifting of restrictions on commercial use of the Internet in 1991.