I'm going to break this response down into 4 sections, Background, Republican violence, Loyalist Violence and Security forces, I'm also on mobile so I apologise ahead of time for any formatting or spelling issues.

-- Background --

The north/south divide with in republicanism became embedded fully during the war of independence, the IRA in the northern most counties had an almost seperate command structure and high level of autonomy that wasn't common in the south, this was because the northern units had to deal with a very different kind of war than their southern comrades. While the south was no stranger to reprisal attacks against civilians the same kind of attacks came with a more sinister twist in the north, sectarianism. Many IRA actions in protestant dominated territory would almost always be followed up with a reprisal killing, burning or bombing of a catholic target and even the ceasefire on the 11th of July 1921 did little to stem the violence. Two days before the ceasefire was to come into effect the RIC (Royal Irish Constabulary) and USC (Ulster Special Constabulary) attempted to perform a search of the Catholic Falls road in Belfast but were ambushed and repelled by an IRA unit, Sunday 10th would be dubbed Bloody Sunday as it would see the deaths of 11 catholics and 5 protestants as vicious battles rages across the city. It was not the first nor last Bloody sunday in Ireland. The following year would see two bouts of killings, the McMahon killings in which 8 Catholics where lined up and shot killing 6, and the Arnon street killings which left 6 catholics dead a week later both in retaliation for the killings of police officers. By the end of the violence 159 Protestant civilians and 258 Catholic civilians, in a region where Catholics made up just over a third of the population.

The killings and the Ulster government's refusal, inability and inadequacy to investigate them or punish those involved lead to heighted tensions with the newly formed 'Southern Ireland', Both Lloyd George , the leader of the UK and Winston Churchill the Secretary of state for war then for the colonies feared that the violence would collapse the statelet in it's infancy and hesitated to force Craig, the prime minister of Northern Ireland into action. This began to contribute to an increasingly hostile view of the northern government not just amongst the people but also the IRA which would split in 1922 and fall into a civil war.

Michael Collins, leader of the Republican forces had been tacitly supporting the IRA in the north, funneling weapons, ammunition and money to them during the ceasefire, he hoped that the threat of IRA violence would force Craig into giving the Catholics better protection from militant loyalists. Collins would negotiate the divisive treaty that caused the Irish civil war which solidified partition of Ireland, ironically the northern units supported Collins and believed the Republic could still be achieved but the civil war and death of Collins left the northern IRA isolated and soon it collapsed under interment.

The IRA in the north would struggle to reignite the war, especially as the south would split and reunify as the years went on, a Republican victory in the general elections had brought Eamon De Valera to power in the Free state and many IRA members believed it was time to relauch the campaign but De Valera instead attacked his former allies and had most arrested. The IRA would split down ideological lines, facist and Conservative nationalists went one direction while socialist and communists went another, De Valera fearing a coup from the military and the 'Blue shirts' released many IRA prisoners who clashed in the streets with their former comrades to the war cry of "No free speech for traitors". Eventually many IRA members travelled to and fought on both sides of the Spanish civil war, most famously in the Connolly column on the republican side.

The movement periodically split with large splinters forming groups like Saor Éire(Free Ireland, a communist group that would give inspiration to many leaders of the 1960s) and Saor Uladh(Free Ulster, that wished to create a parliament for all of ulster under Irish rule) however all fringe elements would subsumed for their campaign during WW2, which failed spectacularly due to ideological divides and lack of German support and the later border campaign, which's failure lead to the marxist takeover of the group.

The north meanwhile had slowly calmed down, sectarian violence decreased but sectarian discrimination increased, a segregated society slowly formed and the Catholic citizens got an increasingly short end of the stick. In order to maintain political control of key areas the protestant Parliament gerrymandered the electoral boundaries and packed catholic voters into increasingly small areas. Derry became an infamous example of this as the Catholic population that made up 2/3 of the city could only capture 1/3 of the seats of on the city corporation as they had been packed onto the westside of the river. The Free state and later Republic was never free of sectarianism either, the much smaller population of protestants almost immediately left for the safety of Ulster, fearing retaliation for their support of the Crown throughout history.

As the riots of '69 raged thousands of refugees poured across the border into the Republic, some from as close as Derrt and other from as far Belfast. The news footage of the camps, burning houses and reports of deaths stirred up memories of the old days and many in the south were enraged, thousands of old weapons were rushed north and into the hands of catholics, IRA members and others willing to fight. In the camps the Irish army began training volunteers to fire and maintain rifles alongside first aid, in what was to be later called the arms crisis £50,000 was siphoned from the relief fund to purchase weapons by future Irish leader Charles Haughey, the vast majority of which came under the control of the new, violent and soon to be infamous Provisional IRA.

This had not gone unnoticed by the protestant population and many now had their fears and suspicions of the Irish government aiding the IRA confirmed, the arrival of the Irish Army to the border had also sparked fears of an invasion, a plan the Irish government did entertain but never left the planning stages. As the conflict progresssd the intial government support the Catholics in the north waned and soon they would give only polictal support, isolating many moderate nationalists and leaving only the IRA as an avenue for change.

-- Republican Violence --

1966, Easter day, up went Nelson. The IRA in a political stunt pilled explosives against Nelsons Pillar in Dublin and destroyed it in honour the Easter Rising 50 years before, it was the first of a spate of violent acts the IRA would carry out.

The Provisonals had rules, one of which was that no hostile action was to be carried out against the Republic of Ireland, this rule applied to various things but not to 'fund raising', throughout the years the IRA would get into gun battles with the Garda(Irish police) and Irish army during robberies, kidnappings or escapes from the British across the border, there were too many of these cases to count and many were nothing special so I'll tell perhaps the oddest.

Shergar was a race house, a successful for that had one a good few races and had a long career of studding ahead of him but on the 8th February 1983 a group of men stormed the home of the groomer, telling him they wanted £2 Million. The police were soon alerted and they began scouring for Shergar and the men who took him, The negotiating team soon encompassed Aga Khan, the leader of the Nizari Ismailism sect of Islam the primary owner, Ghizlain Drion, a frenchman and Khan's site and many radio and tv personalities related to horse racing.