John Clark, a victim of the 1973 Old Bailey bombing in London, Jonathan Ganesh, a 1996 London Docklands bombing victim, and Barry Laycock, a victim of the 1996 Arndale shopping centre bombing in Manchester, all allege Adams was a leading member of the Provisional IRA on those dates, including of its Army Council.
The trio are bringing legal action against the former Sinn Fein president and are seeking just one British pound in damages.
They claim Adams "acted together with others in furtherance of a common design to bomb the British mainland" and was "directly responsible" in various roles within the Provisional IRA for decisions made to place devices in 1973 and 1996.
Adams denies that he had any role in the Provisional IRA and is opposing the claim.
The trial before Mr Justice Swift, due to begin on Monday at the Royal Courts of Justice in London, is expected to last seven days.
Lawyers for the three bombing victims told a previous hearing that Adams should be considered a representative of a class of people who "were members of the Provisional IRA/its Army Council between 1973 and 1996".
The men also wanted to sue the Provisional IRA but Mr Justice Soole said that claim must be struck out because it is "not a legal entity".
Two of the witnesses due to give evidence against Adams will be anonymous and will speak at the trial from behind a screen.
Anne Studd KC, for the three men, told a hearing last month that one of the witnesses believes "the Provisional IRA or people associated with it still exist" and will be in danger as a result.
"This case is very likely to increase interest again in these issues and this witness, with his past experience, is concerned about that," she said.
She also applied to include more witnesses being able to give evidence, which Mr Justice Swift allowed.
26°C