I think it's a little bit tough to pin down an exact point in history when people began studying economics, because like any field it developed slowly and changed over time.

A book that you might find helpful is "The Ordinary Business of Life" by Roger E. Backhouse, which provides a history of economics (you can read the first chapter for free here: http://press.princeton.edu/titles/7247.html).

The earliest economic writing/thinking he points to is in ancient Greece. The word "economics" comes from a text called "Oikonomikos" by Xenophon, a pupil of Socrates. The text was a treatise on how to manage an agricultural estate.

A lot of early "economic" study had more to do with questions of morality rather than the sort of topics economists might study today. For example, when Aristotle discussed something like interest (as in making money off of money), he wrote that it was immoral because it was not a natural form of acquiring wealth in that way, say, farming was.

Sorry if this answer wasn't that helpful. If you have a question about a more specific time frame, let me know and I can try to elaborate.

For now, I'd definitely recommend "The Ordinary Business of Life," as I previously mentioned. I'd also suggest "The Worldly Philosophers" by Robert Heilbroner, which is among the most famous books out there concerning economic history and the foundation of the field.