Caesar, Brutus, their wives, and all sorts of other folks are gathered in a public place. They're ready to celebrate the feast of the Lupercal, an annual party which involves a bunch of Romans dressed in leather loincloths running around the city lashing whoever they find with a goatskin whip. Seriously.
Caesar's friend Antony will be running in the festival this year, and Caesar tells Antony not to forget to "touch Calphurnia." She is Caesar's wife, and the whip is supposed to cure her "barrenness." (Before we forget, this is the same "Antony" who shows up later in Shakespeare's steamy play Antony and Cleopatra.)
After broadcasting his wife's business in the street, Caesar hears a soothsayer (a prophet or fortuneteller) call out to him in the crowd. Caesar now hears the famous warning to "beware the Ides of March," but he ignores it.
Brutus and Cassius meet and talk while everyone else moves on to the next event. Cassius says his good friend Brutus hasn't seemed very friendly recently. Brutus reassures Cassius that "it's not you, it's me," claiming that he's been preoccupied with some thoughts that he'd rather keep to himself.
Cassius then starts to suggest things that Brutus's own humbleness won't let him acknowledge. Cassius hints that Brutus has a reputation for being a really honorable guy, and that everybody agrees about this except Caesar. As Brutus begins to catch the whiff of treachery in Cassius's talk, Cassius assures Brutus he's being serious about the whole "noble" thing and not just flattering him. Without saying so, Cassius suggests that a lot of respected Romans think it would be really nice if someone like Brutus led Rome, even though it would mean "disposing" of Caesar.
Their conversation is interrupted by shouts, and Brutus ends by pointing out that he loves Caesar but hopes the Roman people haven't crowned him king. (Remember, they live in a republic, which has no place for monarchs.)
Brutus adds that he loves honor more than he fears death, which spurs Cassius to continue suggesting they do something to stop Caesar.
Cassius harps on the fact that Caesar isn't any better than them, so they have no reason to be his subjects.
In fact, Cassius says, Caesar is a gutless wonder. Cassius tells a story of how Caesar challenged him to a race on the Tiber River, but Caesar got so tired that Cassius had to rescue him from drowning. Cassius describes how Caesar became sick in Spain, had a seizure, and whimpered. Cassius is clearly implying that Caesar is weak and not fit to be a king.
There's some more shouting that seems to imply that the people are the crowning Caesar, which helps Cassius's cause.
Cassius drives his point home: Brutus is just as good as Caesar, and they would be cowards if they didn't do something to stop Caesar becoming the "first man" of Rome. Cassius then appeals to Brutus's family history. Apparently one of Brutus's ancestors helped establish the Roman Republic by fighting the tyrant Tarquin. Cassius is basically calling for Brutus to uphold the family name.
Brutus promises he's not suspicious of Cassius's motives or flattery but asks him to lay off trying to get him to kill Caesar for a little bit. Brutus will think about whatever Cassius has to say, and he gives Cassius hope with the final thought that he'd "rather be a villager" than call himself "a son of Rome" if things continue on the current path (meaning, if Rome ceases to be a republic). Which would be fine, except Brutus has no interest in being a villager.
When Caesar returns, Brutus notices he and the rest of his crew look pretty unhappy.
Caesar spots Cassius giving him the stink eye and calls out instructions to Antony: he'd like to be surrounded with fat, happy men, because the "lean and hungry look" of Cassius strikes him as dangerous. Antony assures Caesar that Cassius is noble and not dangerous.
Caesar continues to say mean things about Cassius: that he doesn't like music, or smiling, or people who are better than him. (Who is this guy, the Grinch?) Obviously, Caesar has figured out that he should not trust Cassius.
Just then Brutus and Cassius confer with Casca, who has been at the festivities with Caesar. Brutus asks what has put Caesar in such a bad mood.
Casca tells him that the crowd was gathered to watch Caesar receive a (symbolic) crown. Antony offered Caesar the crown three times, Caesar refused it all three times, and three times the crowd cheered wildly (presumably because of the humility of their fearless leader).
Casca thinks the crowd was stupid for not noticing how hard it was for Caesar to resist taking the crown. Each time Caesar refused it a little less wholeheartedly. Apparently the whole thing was so upsetting that it prompted one of Caesar's epileptic seizures in the middle of the marketplace. Caesar had fallen down and started foaming at the mouth, unable to speak.
Even weirder, before Caesar had the seizure, he stood up before the crowd and opened his jacket, offering the crowd his throat to cut. When he came to, he apologized for any weird behavior, blaming it on his sickness, and everyone happily forgave him. Casca is convinced the people would've forgiven him for stabbing their mothers, as they are foolish sheep.
Brutus asks if Cicero, the great orator, had anything to say about this. Casca says Cicero did speak, but Casca couldn't understand it because he was speaking Greek. (Casca, not an orator himself, doesn't know Greek.) Hence the phrase, "It's all Greek to me." (See, you're smarter every day.)
Casca also notes that Murellus and Flavius (remember them from Scene 1?) have been punished. They've lost their positions after their little adventure stripping the people's ornaments off of Caesar's statues. Finally, Casca agrees to have dinner at Cassius's place sometime, though he's pretty rude about it.
After Brutus and Cassius part ways, Cassius thinks he'll convince Brutus to get on the conspiratorial bandwagon eventually, even though the man is noble, or honorable. Cassius is convinced that Caesar treats Brutus with favoritism, making it harder for Brutus to rebel against him. (It's always harder to kill someone who's nice to you.)
Still, Cassius thinks he'll sway Brutus by faking some letters and throwing them through his window at night. The letters will supposedly be from citizens praising Brutus, and, between the lines, Cassius will suggest that Caesar is too ambitious and should be put down by someone like Brutus. Cassius is certain he can shake Brutus's loyalty to Caesar.