Adams became Sinn Fein leader in 1983 when it was the IRA's political wing, establishing himself as the best-known face of the movement seeking to end UK rule in Northern Ireland.
He later reinvented himself as a peacemaker after helping secure the 1998 Good Friday Agreement, which largely ended three decades of sectarian conflict, known as the Troubles, in which 3600 people were killed.
Adams has always denied being a member of the Provisional IRA (PIRA), though he has long faced accusations - including from members of the paramilitary group - that he was involved in its campaign of killings.
The 77-year-old is now being sued by some of those injured in three bombings: one at London's Old Bailey court in 1973, the PIRA's first on the British mainland, and two 1996 blasts, targeting London's Docklands and Manchester.
The three claimants are seeking a nominal 1 pound in damages and a finding that, on the balance of probabilities, Adams was a senior member of the IRA.
Adams' lawyers argued in court documents that there was "no credible evidence to support the claimants' allegation that (Adams) was a senior member of the PIRA".
The claimants' lawyer Anne Studd said on Monday that Adams was "so intrinsically involved in the PIRA organisation that he is as culpable for the assaults ... as the individuals who planted and detonated the bombs".
She cited Adams' attendance at high-level meetings with the UK government in the early 1970s as supporting evidence although Adams says he was there as a Sinn Fein representative.
Studd also said Dolours Price, one of nine people convicted over the Old Bailey bombing, previously accused Adams of involvement in the bombing campaign in Britain.
But Adams' lawyers said Price, who died in 2013, was motivated by a desire for revenge against Adams, whom she believed had betrayed the republican cause through his involvement in the peace process.
They added that Adams had expressed support for supporters or members of the PIRA and its campaign but that did not mean he was a member or "come close to constituting evidence that (Adams) was responsible for the three bombings".
Adams, who sat in court wearing a Palestinian flag pin, is expected to give evidence later this week.
After helping to swing the IRA and the province's Roman Catholic minority behind the Good Friday Agreement, Adams became a member of the Northern Irish Assembly and then the Irish parliament, standing down as head of Sinn Fein in 2018.
The case could prove an unwelcome distraction for Sinn Fein, currently the largest party in the Northern Irish Assembly and the main opposition south of the border as it pursues its goal of a united Ireland.
