In the moments following Caesar's death, what do the conspirators proclaim to justify their deed?
One of the most interesting points, which is usually overlooked in the death of Caesar, is the historical connection between Marcus Brutus and the the start of the Republic.
At first, Rome started off with kings. According to Livy, there were seven original kings and their tyranny became so great (last king in particular) that they were overthrown as the only solution. At that point, the Republic was born. Moreover, the Republic was structured in such a way that it did not allow for a king to emerge again. There was always a pairing of power. The two highest officials, who were elected every year by vote, were called consul. The first consul was Lucius Junius Brutus.
This name is very important, because his great descendent was Marcus Brutus, one of the conspirators who killed Caesar; he was also made famous by the play of Shakespeare (of the same name).
In light of this family connection, Marcus Brutus by killing Caesar wanted to restore the glories of the Republic. He was, in fact, doing exactly what his ancestor did. Freedom from tyranny was the point.