"The English-speaking world is divided into those who have read THE LORD OF THE RINGS, and those that is going to read it." - Sunday Times.
Assuming you fall into first category a synopsis is redundant, and assuming you are in the second category it is a spoiler. Simply summed up then Fellowship of the Ring is the continuation of THE HOBBIT OR THERE AND BACK AGAIN, which recounts the (mis)adventures of a hobbit, Mr. Bilbo Baggins and a ring. FELLOWSHIP, focuses on Bilbo's heir Frodo Baggins who when Bilbo in his aged state decides to leave his home in Middle-Earths shire, home to hobbits, leaves everything to Frodo. The mysterious yet kind wizard Gandolf drops hints to Frodo that the magic ring is not some parlour trinket, but of a dark design once owned by the evil Sauron, who seeks to claim "the one true ring to rule them all again." Hence Frodo and his friends begin their journey to destroy the Ring before the forces of evil can destroy them.
Might be hyperbole, but this is debatably the greatest fantasy epic ever written. The measuring stick against which all fantastic tales written since has been measured. Tolkien's gift of language and descriptive detail is second to none, possibly he was a magician in England conjuring stories in reaction to his keen distaste for what he saw the Industrial revolution doing. Read in that context adds an additional layer to a tale into which depths more than one hobbit, elf, dwarf and yes human has fallen.