The original iPod was released in October 2001 after a year of development (meaning that the answer to the question "when was the iPod invented" is roughly 2000).
Read Apple’s press release for the original iPod.
When the iPod was introduced, it was met with mixed reactions. Some loved it, while others thought it was too expensive, that its Mac-only status (in those days; that changed soon enough) would limit it, and that it ought to include wireless features. Hindsight’s 20/20, right?
The second-generation iPod, which added Windows support, was introduced in summer 2002, followed by the third-generation iPod in April 2003.
The iPod mini--the first offshoot from the original iPod line--debuted in January 2004. Since then, new models have been released roughly every six months on a fairly consistent schedule.
For a timeline detailing when iPod models have been released and retired, check Wikipedia’s Timeline of iPod models.