Satoshi Nakamoto is the name used by the person or people who designed bitcoin and created the original reference implementation now called Bitcoin Core (formerly known as Bitcoin-Qt).
In October 2008, Satoshi Nakamoto published the Bitcoin whitepaper, entitled "Bitcoin: A Peer-to-Peer Electronic Cash System." The paper was published to a cryptography mailing list describing a "new electronic cash system" which as come to be bitcoin the digital currency. Nakamoto released the first bitcoin software version. The first bitcoin transaction took place on the blockchain on January 3, 2009.
Embedded into the first bitcoin transaction was a message from Nakamoto which read "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks" which is view-able in a blockchain explorer when looking at bitcoin transaction 4a5e1e4baab89f3a32518a88c31bc87f618f76673e2cc77ab2127b7afdeda33b. The first transaction is part of the Genesis block.
Nakamoto continued to work on the bitcoin project until he mysteriously disappeared in 2010. His last message ever publicly made  was to the SourceForge Bitcoin Mailing List where he added changes to help with DoS protection. Before his departure, Nakamoto handed over control of the bitcoin development to Gavin Andresen.
Since Nakamoto's real identity has never been revealed, several people over the years have been named as possible Satoshi Nakamoto candidates, but to date there has been no definitive proof that any of the names below are actually Satoshi Nakamoto.
- Hal Finney 
- Nick Szabo 
- Wei Dai 
- Dorian Nakamoto 
- Ross William Ulbricht 
- Shinichi Mochizuki 
- Craig Steven Wright 
- Nakamoto's last public message, posted to the SourceForge Bitcoin Mailing List (December 13, 2010)
- Robin Hanson, "Conspiracy Theory, Up Close & Personal" March 25, 2014
- Nathaniel Popper, "Decoding the Enigma of Satoshi Nakamoto and the Birth of Bitcoin" (May 15, 2015)
- LikeInAMirror, "Occam’s Razor: who is most likely to be Satoshi Nakamoto?" (March 11, 2014)
- Leah Mcgrath Goodman, "The Face Behind Bitcoin" (March 6, 2014)
- John Markoff, "Study Suggests Link Between Dread Pirate Roberts and Satoshi Nakamoto" (November 23, 2013)
- Ted Nelson, "I Think I Know Who Satoshi Is" (May 17, 2013)
- Andy Greenberg, Gwern Branwen, "Bitcoin's Creator Satoshi Nakamoto Is Probably This Unknown Australian Genius" (December 8, 2015)