The other Senators saw Caesar as a tyrant. He had made himself Dictator for Life and wore purple, a colour strongly associated with the Roman kings. He styled himself too much as a monarch for their comfort, so they hoped in killing him it would restore the Republic. Dictators were reserved for times of crisis and of course there was no crisis. They also only lasted 6 months, which is why he was assasinated after that time.

As for why it wasn't restored, it is important to understand the way the Roman army worked. The soldiers were fiercly loyal to their general as they needed them in order to secure veteran settlement once they retired. The Senate didn't have it's own army, and so after the death of Caesar it had to play generals off against each other - Marc Antony against Brutus Decimus , Hirtius, Pansa and Octavian against MA and then finally supported Brutus (not Decimus) and Cassius against MA and Oct.

So why couldn't the Senate just make its own army to fight the most powerful general instead of playing them off against one another? The Romans had a patronage-client system and all laws passed were in the name of the proposer of it. With the client-patronage system a patron would give breakfast, legal support and ensure a job for their clients and in return they got politcal support. If a Senator proposed making a Senate army they would gain all the soldiers as clients, making them significantly more powerful.

So really, the Republic was dead no matter what. It needed to change for the Roman State to survive, thus Augustus transforming it to empire.

While I agree with the general consensus here I would have to disagree on a couple finer points.

To understand this period with the best clarity you have to go backwards a couple generations. Obliviously Caesar, Brutus, Pompeius, Crassus and Antony didn't exist in a bubble however I find so many times discussions tend to focus on just their generation. While the anti-king rhetoric was convenient with Roman ideals and understandable to your average citizen the upper class were afraid of something a lot more real to them then a mythical king. I would postulate that the upper classes were not so afraid of Caesar becoming a king as they were of him becoming another Sulla. Rome had already been through several tyrants. Sulla epitomized the ideal conservative (read as hyper Senate controlled) and tried to reform the government to reflect these ideals. Caesar leans towards the exact opposite pushing for more fair representation between the Senators, equestrians and plebeians.

The senators, many of whom remembered Sulla, had to have a feeling the reckoning was coming. Sulla's proscriptions (state sanctioned murders where the entirely of the persons estate becomes the property of the state) had murdered huge numbers of prominent citizens with a special focus on the Marian faction. That Marian faction, the populares, were roughly the same group championed by Caesar a generation later. A lot of Caesars clients had had their fathers, uncles and grandfathers murdered.

Given the well known fact Caesar planned on heading East to fight the Parthians you could speculate that Caesar's murderers knew they had a bit of a time crunch on their hands. A far easier man to kill in Rome what would happen to the Senators if Caesar was again successful in his military campaigns? He would be by far the richest man in Rome (far more so than he was already) and would have an even larger number of clients and wealthy former soldiers in his corner. Any attempt to kill him or politically fight him at that point would be impossible. The senators would have another Sulla, but this time one that was not on their side.

While the narrative points to these lofty ideals I tend to think of those as propaganda. The motive wasn't so much personal gain as it was self-preservation. Their eventual goal would have been to re-reform the government to how it was left under Sulla, with the Senate in full control with little equestrian and plebeian involvement.

To add a little more to what /u/Calanon said, the Roman people had very strong feelings towards the institution of a king, this was evident in all Roman classes but was more so in the upper, patrician class because the institution of a king would deny them a chance at power that was usually supplied by the cursus honorum translated to "ladder of honour" where they could gain prestige and power to control armies throughout their climb to becoming a candidate for consul.

What Caesar had essentially done is set the ball rolling to form an empire, just prior to his death he began introducing potential heirs to the power he possessed and gave them some honours that they may not have deserved.

As with most things in the world there were many factors that contributed to Caesar's assassination, most notably is that he gave the people of cis-alpine and trans-alpine Gaul cititzenship that he had promised many years before when he was gathering supporters that he could later use to form legions. The Roman senate were hyper-nationalists and they objected to the introduction of non-Romans into the Roman way of life.

In the same way Caesar introduced a larger senate to help him further his agenda, as with citizenship being in the senate was sought after because there were only 600 seats for all of the patricians in Rome. Caesar increased that count to 1000 and filled those seats with people loyal to him, many of whom had come from Gaul.

It'd be naive to say that the end of Pompey's marriage was the tipping point for open hostilities. Caesar's growing power had long worried the senate and the end of Pompey's marriage was just the breaking down of another barrier to all-out war between Pompey and Caesar.

So in summary the senate didn't believe that the assassination of Caesar would "magically" bring the Roman republic back but it did go a long way to make it more difficult for Octavian to institute himself as princeps.

I asked the same question on a different account about Pompey's marriage and got this really helpful and well-informed answer

To add to /u/Calanon and /u/BassKiwi's answers, it's useful to remember that Republican politics were fraught with aristocratic self-interest. The elites of Rome are highly engaged in competition and interested in self-representation in the public sphere. With Caesar as dictator, Roman elites were not able to exercise their own agendas without fear of reprisal. Roman politics were also fraught with violence and the very real threat of violence. "Restoring the republic" or "dethroning a tyrant" are claims that allow one to exercise power in a manner that seems legitimate and beneficial to the survival of the state and the Roman people. That isn't to say that the person making these claims didn't authentically believe that these were the correct actions to take.

If anything the whole plan seemed a bit naive in that they all kind of expected the republic to be magically restored and had no plan for after Caesar's death.

I'd be interested in answers to this point as well.

IIRC the conspirators killed Caesar and then occupied the Capitol (which I have seen being interpreted as a symbolic move motivated by the fact that in Greek cities the Akropolis actually mattered).
What exactly did they expect to happen at that point? Why didn't they do something sane like taking control of the curia (as Tarquinius Superbus is said to have done) while they had the moment of surprise? Why no proscriptions to force the Caesarians out of the city? The whole thing just seems incredibly badly planned.

All these answers but no sources.