US First Lady Michelle Obama and her daughters began their visit to Dublin this morning with a trip to Trinity College.
Mrs Obama said she "expect great things" of the young people of Ireland and that she has "never felt more optimistic" about our island.
After arriving at Dublin Airport on Air Force One she was whisked to Trinity along with her daughters Malia (14) and Sasha (12) to study their family heritage and see the Book of Kells.
The visit caused significant traffic disruption in the city centre as gardai temporarily closed off roads.
The Obamas arrived in Belfast at 8.30am this morning and Michelle began a hectic day by introducing her husband, Barack, to secondary school students at the city's Waterfront Convention Centre.
She spoke of their "pretty packed schedule" over the next few days but said that it was an "honour" to be so welcome in Ireland.
"But wherever we go, no matter what's on our plate we always do our best to meet young people just like you.
"You might be some of the most important people that we talk to on our trip," she said.
"When I look around this room I don't just see a bunch of teenagers, I see people who will be moving the world forward in years to come."
She told how neither she nor Barack could ever have imagined living in the White House.
Officially the US embassy said that Mrs Obama was on a "private visit" to the east coast while her husband attends the G8 Summit of world leaders in Fermanagh.
After her address in Belfast this morning she flew to Dublin and was escorted under heavy security from the airport to Trinity College.
The family received a guided tour of the Old Library where they will be shown documents from the archives relating to Mrs Obama's Irish ancestry, and the Book Of Kells. They are due to attend a performance of Riverdance at The Gaiety Theatre this evening, along with Ireland's First Lady, Sabina Higgins, and Taoiseach Enda Kenny's wife Fionnuala.
Tomorrow, the Obamas will be taken on a tour of Glendalough in Co Wicklow before having lunch in Dalkey.
After lunch, Mrs Obama and her daughters are due to fly back to Belfast.
A large number of rooms have been booked at The Shelbourne Hotel on St Stephen's Green for the entourage tonight.
The city faces traffic disruption during the visit. The longest diversions will be around the Shelbourne Hotel.
Gardai said peaceful protests would be facilitated but that plans had been drawn up to deal with any troublemakers.
City-centre traffic arrangements include closing Kildare Street until Tuesday evening with local access only.
Dublin Bus vehicles will rejoin their routes via Hume Street/St Stephen's Green or Merrion Square east.
Parking restrictions will be in place on St Stephen's Green east and north and Molesworth Street until tomorrow evening.