Many forms of football that have been played in human history.
The Chinese version, called cuju, is the earliest form recorded, with rules standardized during the Han Dynasty (206 BC - 220 AD). Phaininda and episkyros were ancient Greek football games and the Ancient Roman game, harpastum, was described in 228 AD.
However, as the question is specifically talking about Soccer the history of that specific form of football began with the man who drafted the 'Laws of the game' for Soccer or 'Association football.' This was Ebenezer Cobb Morley. Ebenezer who, along with other co-authors, agreed to the rules at a public house called the Freemasons Tavern in London on 26th October 1863.
The main object of the FA was to standardize the many forms of football that were played in England at the time. Morley became the Football Associations first secretary. He has also founded the Barnes Football Club a year earlier in 1862 which he captained against Richmond football club in the first ever soccer match on 19th December 1863. The game ended 0-0. He died in 1924 and is buried at a Cemetery on Barnes Common not far from where he drafted the Laws of the game at 26 The Terrace, Barnes, London. A blue plaque commemorating his life's work was placed on the wall of this address by English Heritage in 2009.
The word soccer is a phonetic abbreviation of the word 'Association' coined by English public school students who took the 'soc' from 'Association' and put an 'er' on the end. That is why prior to 1863 the word soccer did not exist. It is probably worth noting that the same students called Rugby football 'Rugger' but this word fell out of use.
I don't know the exact inventor of soccer, though what I do know, is that it was invented in England. I think it was a number of people who invented soccer and not just one person. Look at the question (on this site) Where Did Soccer Originate? I answered that question and it has more information on where it originated and the spread of soccer over the years from when it was invented. (I am not completely sure when soccer was invented though).
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