Britain's Queen Elizabeth II has finished the last of her public engagements on the first day of her State Visit to the Republic of Ireland.

President Mary McAleese and Queen Elizabeth laid wreaths at the Garden of Remembrance this afternoon.

The wreath-laying ceremony at the garden, which commemorates those who died in pursuit of Irish freedom, was followed by one minute of silence.

They were greeted there by Minister for Defence Alan Shatter and the Chief of Staff of the Defence Forces, Lieutenant General Sean McCann.

The Queen then made the short journey to Trinity College, where she viewed the Book of Kells and met students and staff.

The visit to the college was her last public engagement of the day and she has returned for a private evening at Farmleigh House in the Phoenix Park.

Earlier, the plane carrying Queen Elizabeth and her husband, The Duke of Edinburgh, touched down at Casement Aerodrome in Baldonnel at 11.57am.

The visitors were welcomed by Tánaiste and Minister for Foreign Affairs Eamon Gilmore, the Irish Ambassador to Britain Bobby McDonagh, the Deputy Chief of Staff Major General Dave Ashe and the GOC of the Air Corps Brig General Paul Fry.

The visitors walked along a red carpet and through a guard of honour of 30 Air Corps personnel.

Queen Elizabeth was presented with flowers by eight-year-old Rachel Fox from Shankill in Dublin.

The Queen then travelled to Áras an Uachtaráin for a ceremonial welcome. She planted a tree to mark her visit and had lunch with President Mary McAleese.

Security and traffic arrangements

A huge security operation is in place in Dublin and a number of roads around the capital were closed for several hours today.

O'Connell Street and the North and South Quays have reopened to traffic having been closed for much of the day.

Gardaí arrested 21 people following violent disturbances at the top of Parnell Street during the Queen's visit to the Garden of Remembrance.

One person was released without charge, but the remaining 20 appeared in court this evening charged with public order offences.

The trouble began at around 1.45pm when demonstrators at the top of North Frederick Street began throwing missiles at unarmed uniformed gardai manning the barricades.

The public order unit was deployed and the demonstrators were moved back up Dorset Street and Blessington Street and onto the surrounding areas.

Bottles, rocks, fireworks and other missiles were thrown at gardaí, although there are no reports of any injuries.

Bins were overturned and refuse bags were set on fire as gardaí moved in and arrested individuals for public order offences.

Officers say that many of the troublemakers are known to then. The disburbances continued for three hours this afternoon

Luas services return to normal

All services on the Luas Red Line have returned to normal after a security alert in Dublin, while there was also a security alert in Maynooth overnight after a viable explosive device was found.

Speaking on RTÉ's Morning Ireland, Taoiseach Enda Kenny said those opposed to the visit were entitled to protest, but added that he hoped they would not embarrass the country.

Former Taoiseach Brian Cowen said the visit marked the relationship of understanding and respect between both countries.

Dublin Bus services will operate as normal during the State visit.

But the company says that, due to traffic restrictions, there will be diversions and possible delays to some services in the city centre area from today until Friday.

Iarnród Éireann has also advised passengers that there could be some delays but expects these to be minimal.

Click here for AA's traffic updates

King George V, Queen Elizabeth's grandfather, was the last British monarch to visit Dublin in 1911.