The Beatles started in 1956 as a group formed by John Lennon and his school friends called The Quarrymen(named after the school all of the members attended).in July of 1957,Paul McCartney(at the urging of his friend and Quarrymen member,Ivan Vaughn,who told him it was a good place to pick up girls)went to the Woolton Village Fete to see the group play,after the show Paul played guitar backstage(the song in question being 20 Flight Rock)and the members were impressed for 2 reasons:1.Paul could tune a guitar(they had to go to a music pro on Kings Road to get theirs tuned)and 2.Paul actually knew the words,on the strength of these 2 things Paul was asked to join the band.In 1958,Paul brought in his friend,15 year old George Harrison to join the bad.However by 1959,pretty much all of the Quarrymen had left the group,just leaving John,Paul,and George.The group did acquire a new bass player in John's art school friend,Stu Sutcliffe(he was persuaded to spend the money he had won in an art competiton on a bass guitar).The lasting impression that Sutcliffe left was that it was he(along with John)inspired by Buddy Holly's group,The Crickets changed to The Beatles.The 1st variations of this name change(their friends advised them against the name change) was seen in May of 1960,at an audition for Larry Parnes to be the backup group for Billy Fury.After going through several variations of the Beatles name(as well as several drummers),in August of 1960(before going to Hamburg)after acquring Pete Best as their "permanent"drummer,they started going by The Beatles,it was during this 1st trip that The Beatles became friendly with Ringo Starr,the drummer of The Hurricanes.It was during one of The Beatles early trips to Hamburg(1961)that Stu left the group and Paul became the bass player.Throughout 1961,The Beatles were still frindly with Ringo Starr and in fact during that year and even in 1962,Ringo would actually sub for Pete for various reasons.Finally in August of 1962(in what some fans call a shameful act)Pete was let go and Ringo was brought in,thus cementing the now familiar Beatles line up.
Now as to why The Beatles broke up,read this link for my reasons why:https://answersrip.com/question/index?qid=20100316203238AARQ8bP&show=7#profile-info-0BctsGvkaa
As you can see it got best answer.
Now for the simple reason why The Beatles broke up:They broke up due a dispute between Lennon and McCartney,everyone else involved in the breakup(George,Ringo,The Eastmans,Yoko Ono,Allen Klein,and even Phil Spector)was caught in the middle!