To calm the crowd, he tells them that he is not here to praise Caesar. He continues with an aphorism saying that after one dies people only remember the bad things about him and they forget all the good things he has done, a subtle allusion to Julius Caesar. He is ironic: he repeatedly calls Brutus "noble" and "honorable". He says he doesn't deny that Brutus is an honorable man and that Brutus blames Caesar for ambition and then he expresses doubt about all that with an "if": "If it were so". We notice that, a great orator, he never says directly what he has to say; he only insinuates things and makes the auditorium put the pieces together. He continues by saying that only under the permission of Brutus he came to speak; he displays modesty, but it's a would-be modesty.
Mark Antony speaks about Caesar's successes, about the good and clever leader he was. He reminds Caesar's qualities and, knowing that the people are responsive to material interests, he tells them that Caesar would not take the crown, in order to inflame them against the conspirators. Then he uses a rhetorical question to cast doubt upon the blame put on Caesar: "was this ambition?". Using the adversative conjunction "yet", he is putting face to face the facts with Brutus's affirmations. We notice the emphatic use of "do", a rhetorical device, in "what I do know", to clear any doubt about the rightfulness of his words; and another emphatic word, "did", in "You all did love him".
Antony makes a rhetorical invocation: "O judgement!"; he is now histrionic; he acts, forcing the approval of the people: "My heart is in the coffin there with Caesar,/ And I must pause till it come back to me.