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Michael Higgins is the first Irish President to make a state visit to the UK, ending the day with a state banquet at Windsor Castle.
Today's historic visit is a symbolic ending to the painful separation of British and Irish states, but 3000 unsolved murders remain.
The Queen and the Irish President Micheal D Higgens have been viewing Irish items in the Royal collection in Windsor as part of the historic state visit.
President Higgins will address the Houses of Parliament later this afternoon, before the royal banquet this evening.
The Queen and the President of Ireland stood side by side to observe the Irish Anthem being played by a military band in Windsor, during the first visit to the UK by an Irish head of state.
The anthem was played after the President Higgins and Michael Higgins were honoured with two separate gun salutes, and Mr Higgins and Philip inspected troops of the Queen's Company, Genadier Guards.
Major Andrew Seddon, captain of the Queen's Company Grenadier Guards, invited Mr Higgins to inspect the guard of honour, speaking to him in Irish. The Irish Guards was represented by their regimental band as the troops are currently on peacekeeping duties in Cyprus.
President Higgins presented a new ceremonial red coat to its regimental mascot, an Irish wolfhound called Domhnall of Shantamon.
The Irish flag is hanging outside Windsor Castle as the Queen prepares to welcome the Irish President for the first state visit in history.
Crowds have started to gather along the route, ahead of Micheal D Higgins' momentous meeting with the Queen.
Although President Higgins has travelled to events in London, Manchester, Liverpool and Scotland last year, these were not official visits.
Today's ceremonial visit will begin at the Irish Embassy, when the Prince of Wales and The Duchess of Cornwall will greet The President and Mrs Higgins, on behalf on the Queen.
They will then journey together to Windsor.
Irish President Michael D Higgins said today's historic state visit to the UK was not about "forgetting the past" or "wiping the slate clean" but about focusing on the present and building future relations. It is the first official state visit from Ireland to its former colonial ruler.
Speaking to Irish state broadcaster RTE he said progress should not be about forgetting the past.
"The challenge is to hand to a future generation all of the prospects of the future. You are not inviting them to an amnesia about any deep dispute.
"There are a lot of very difficult memories and it would be to my mind wrong to suggest to anyone that you should as it were, wipe the slate clean."
The President will be joined on the trip by Irish Taoiseach Enda Kenny and Foreign Affairs Minister Eamon Gilmore.
Sinn Fein could not "be seen to say no" to Martin McGuiness' controversial invitation to the state banquet thrown in honour of the Irish President at Windsor Castle, a politics expert told Daybreak.
Mark Hennessy, the London editor for the Irish Times, expected "the vast majority" of people in the Republic of Ireland would be "pleased, perhaps slightly irritated" that the high profile invite had overshadowed the historic state visit.
The Irish President said he will be "affirming and celebrating" the values Britain and Ireland share on his state visit to the UK this week.
Ahead of his state visit, Professor Higgins said:
– President Higgins
This historic visit reminds us that while the passage of time can change the contours of political maps and perhaps even community allegiances, it does not alter the challenges and possibilities of our shared humanity with its innate decency and dignity.
The values which unite the British and Irish people are ones I look forward to affirming and celebrating during the forthcoming State Visit to the United Kingdom.
Irish President Michael D Higgins will meet the Queen at an official banquet held at Windsor Castle as his state visit to the UK begins.
The president and his wife, Sabina, will be the guests of the Queen and the Duke of Edinburgh at Windsor Castle for the four-day visit.
Northern Ireland's deputy first minister, Martin McGuinness, who did not meet the British monarch during her Dublin visit, will be present for the state banquet, along with amongst others, First Minister Peter Robinson, Prime Minister David Cameron and Taoiseach (Irish prime minister) Enda Kenny.
This is the first state visit by a head of the Irish state and marks the "maturity and warmth" which has grown between the two countries, Mr Higgins wrote last week.
Queen Elizabeth was the first British monarch to visit Ireland in May 2011.
Martin McGuinness has described his decision to attend a banquet hosted by the Queen as "an important thing to do" that sends "a message to everybody about how things have changed".
Speaking today, the Northern Irish Deputy First Minister and former IRA commander said that "both governments, who have been rather sluggish over the course of recent times, would do well to learn the lessons of what is happening here in the course of next week".
"They have a huge responsibility to play and unfortunately they haven't been playing it in the last number of months," he added.
Mr McGuinness, who shook the Queen's hand in an historic first meeting in June 2012, said: "We're not just involved in a peace process - we're also involved in a change process.
He added that his acceptance was "an attempt by me to stretch out the hand of friendship" to the unionist and loyalist communities of Northern Ireland.