How were letters sent before there were stamps? Who invented stamps?

It all started in England

The first postage stamps for the prepayment of letter postage were issued in England in 1840. This came about following a competition to derive a pre-paid service under the guidance of Rowland Hill, who successfully proposed them in his pamphlet Post Office Reform (1837). 

Postal charges at the time were determined mainly by the distance traveled (and the weight of the letter), but Hill proved that the main cost of transport was in the handling and sorting of letters rather than in their carriage.

Hill further observed that, because most letters went through post unpaid and postage had to be collected from the recipient on delivery, many of them were refused and had to be returned, thus necessitating a two-way trip for no revenue. 

Hill proposed a radical change: that all postage be prepaid, and that letters be carried any distance within Great Britain for a fixed rate (which he suggested be a penny for each half-ounce). 

With the backing of the Exchequer, Hill had two devices made: prepaid envelopes, and, for those wishing to use their own stationery, adhesive postage stamps. The prepaid envelopes were laughed out of existence owing to their ridiculous designs, but the stamps were an immediate success: a one-penny design in black and a two-penny one in blue, both bearing a profile of Queen Victoria, went on sale to the public on May 1, 1840, and were good for use from May 6.

First Dealer

Jean-Baptiste Philippe Constant Moens (died in 1908) was a Belgian philatelist recognized as the first dealer in stamps for collectors.