Beate Zschaepe is the only surviving member of a three-person neo-Nazi group, the National Socialist Underground, which was discovered only in late 2011.
She is also accused of involvement in 15 armed robberies, arson and attempted murder in two bomb attacks.
The 38-year-old denies the charge of complicity in the murders of eight ethnic Turks, a Greek immigrant and a German policewoman between 2000 and 2007.
The case has led some in Germany to wonder why police took so long to link the murders, with critics accusing them of turning a blind eye to neo-Nazi crimes.
The case only came to light after Ms Zschaepe's alleged accomplices, Uwe Mundlos and Uwe Boehnhardt, were found shot dead in an apparent murder-suicide.
She then allegedly blew up their shared home in eastern Germany and later surrendered to police.
A DVD emerged with a film in the style of a Pink Panther cartoon in which the group claimed responsibility for the attacks.
A probe into the handling of the case revealed oversights and mistakes by police and domestic intelligence services and a realisation that the right-wing extremist threat had been grossly underestimated, AFP reports.
Germany has not seen a terror trial of this scale since members of the left-wing militant group, the Red Army Faction, were sentenced 36 years ago.
Hundreds of black balloons filled the sky over the courthouse, and dozens of anti-racism protesters shouted slogans and held large photos of the 10 victims as the trial began.
