Image copyright PAUL FAITH/AFP Image caption The royal couple cradle pints of Guinness at the end of the first day of their visit to Ireland

The Duke and Duchess of Cambridge have ended the first day of their first official visit to the Republic of Ireland with a pint of the black stuff.

The royal couple arrived at Dublin Airport for the three-day trip on Tuesday afternoon.

They began the visit by meeting Irish President Michael D Higgins at his residence, Áras an Uachtaráin.

The day ended with Prince William speaking some words of Irish at the Guinness Storehouse in Dublin.

The Duke of Cambridge opened a speech at a reception, attended by guests from the worlds of sport, film, television and the armed forces, by saying: "Ladies and gentlemen, a dhaoine uaisle [noble people]."

Image copyright Getty Images Image caption The duchess continued to honour the host country with the colour of her evening attire

"We are very much looking forward to our next two days in Ireland, where I have no doubt we will continue to be impressed by the creativity, warmth and hospitality the Irish people have to offer," he added.

After his speech, the duke raised his pint of Guinness and took a sip as he uttered the Irish toast "Sláinte".

During their earlier meeting with President Higgins, the duke and duchess discussed the implications of Brexit.

They also chatted about building on the foundations of the Good Friday Agreement, which ushered in peace in Northern Ireland, a spokesman for the president said.

The duke and duchess attended a string of formal events during the day, including meeting Taoiseach (prime minister) Leo Varadkar at the country's government buildings.

They travelled to the Garden of Remembrance in Dublin - dedicated to people who fought for Irish independence - where they laid a wreath.

Their handwritten message on the wreath read: "May we never forget the lessons of history as we continue to build a brighter future together."

Image copyright AFP Image caption Irish President Michael D Higgins and his wife Sabina Coyne showed the royal couple around the grounds of their residence

Image copyright Reuters Image caption The duke and duchess rang the peace bell at Áras an Uachtaráin

Image copyright AFP Image caption The couple paid their respects at the Garden of Remembrance in Dublin

Royals pay tribute to Irish dead

At the scene - Amy Stewart, BBC News NI

It may be a chilly day in Dublin but the sun came out for the duke and duchess.

Their visit to the Garden of Remembrance, where Irish people remember those who fought for independence, was not open to the public but a modest crowd gathered outside nonetheless.

They were treated to a piper playing an Irish lament before a cheer erupted.

They had arrived - and to a warm welcome.

Almost a decade after the Queen bowed her head and laid a wreath at the Garden of Remembrance, the next generation of royals repeated the gesture.

It may not have had the same significance as 2011's turning point in Anglo-Irish relations but it was another step in continuing the friendship.

Read more from Amy: What do William and Kate hope to achieve in Ireland?

Image copyright Reuters Image caption The duke and duchess met Ireland's Taoiseach Prime Minister Leo Varadkar and his partner Matthew Barrett

Image copyright Reuters Image caption The duchess made a new friend in the form of one of President Higgins' Bernese mountain dogs

Among those watching at the Garden of Remembrance was Melissa Garza, from Texas.

"I saw this was on the list so I came along to see them," he said.

"It was great and so important to lay a wreath like the Queen did."

Hilary, from County Monaghan, said she was "disappointed" in the number of people who tried to catch a glimpse.

"It was a poor enough crowd - maybe people didn't know or they were busy.

"Maybe Dubliners are indifferent."

Helena, from Dublin, watched as her partner made up part of the guard of honour for the ceremony.

She said she would have come anyway as it was "lovely to see Kate and William".

Image copyright Julien Behal Image caption The Duke and Duchess of Cambridge were suitably dressed for their visit to the Emerald Isle

The royal visit aims to highlight the "many strong links between the UK and Ireland", Kensington Palace said.

During their stay, the couple are visiting Dublin, Galway and counties Meath and Kildare.

They have visited Belfast on a number of occasions and last month Catherine returned to Northern Ireland, where she met children at an open farm in County Down.