The strength of Shakespeare is his characterization, and in this play, his strength has the fullest impact. Several eminent critics - not ordinary reviewers like us - claim that Shakespeare was better in characterization more than the plot. So be it.
It is one of the finest Shakespearan tragedy, modelled on historial facts. However, there was a lot of deviations from the history. For example, Ceasar was actually murdered in the Capitol, while in the play, it is the Senate. Such deviations are perfectly acceptable, and are a part of poetic licence.
Although the title is Julius Cesear, the main character in the play is Marcus Brutus. Around him, the plot evolves. There has been a lot of controversy regarding the justifification of the title, but I will not go into that. The fact that in a 5 act play, Ceasar is murdered in Act 3, Scene 1, makes a lot of people doubtful in the title.
Plot: Brutus is a close friend of Ceasar, and a nobleman at heart. He is a true patriot, and puts interests of Rome above self. However, there are a lot of people in Rome having personal grudge against Ceasar. Cassius, Casca, Cimber etc. These people with vested interest convinced Brutus that Ceasar was a tyrant and oppresor, and guiled him to take up arms against Ceasar. They assassinate Ceasar on March 15 (the ides of March). It is during this time that Et tu Brute was pronounces, and it is still said of people who betray others trust.
Then Brutus makes a speech to convince the Romans that Ceasar was ambitious, and was hurting the interests of Rome. Then, Mark Antony, an aide of Ceasar, with his sublime pedagogy provokes the people to rise and revolt against the murderers and butchers. The people drive them away, and then a battle followed, in which Brutus committed suicide.