The Queen stepped out for the first solo outing of her four-day visit to Scotland on Tuesday.
The monarch, 95, held an audience with the First Minister of Scotland, Nicola Sturgeon, at the Palace of Holyroodhouse.
Earlier in the day, the Queen's grandson, the Duke of Cambridge, carried out a solo engagement in Glasgow, visiting the BAE Systems shipyard to see HMS Glasgow in construction.
In Edinburgh, Glasgow and Stirling, Her Majesty will visit businesses, charities and cultural institutions that highlight the pioneering work taking place to further community engagement, education, technology, and efforts to combat climate change.
She is staying at her official residence, the Palace of Holyroodhouse, in Edinburgh during Royal Week, also known as Holyrood Week.
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Her Majesty donned a blue patterned dress for her socially distanced meeting with the First Minister.
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The Queen also receiveed Presiding Officer of the Scottish Parliament, Alison Johnstone, during an audience at her official Scottish residence.
The Duke of Cambridge visited BAE Systems yard in Govan, Glasgow to meet the team building HMS Glasgow on the banks of the River Clyde.
During a speech, he announced that the Queen has approved the appointment of the Duchess of Cambridge as Sponsor of HMS Glasgow, which is the first of the City Class Type 26 Global Combat Ships to be built for the Royal Navy.
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After touring the ship, the Duke said: "My family's affection for the Royal Navy is well known, and as I saw the work taking place here today, I was thinking of my grandfather, the Duke of Edinburgh. He would have been fascinated and very excited to see such advances in skills and technology being put into practice.
"Today, I'm very pleased to announce that my family's connection with Type 26 will endure for many years to come.
"Her Majesty The Queen has approved the appointment of my wife Catherine as Sponsor of the superb ship we see taking shape outside – HMS Glasgow. I know that Catherine will be delighted to join you here in Glasgow for the naming ceremony in due course."
At the end of his visit, the Duke was presented with models of the ship for his children, Prince George, Princess Charlotte and Prince Louis, to paint.
The Queen then visited Stirling Castle to reopen The Argyll and Sutherland Highlanders' Museum in her capacity as Patron of the Argyll and Sutherland Highlanders Regimental Association.
Her Majesty was named Colonel-in-Chief of The Argyll and Sutherland Highlanders on her 21st birthday by her father, King George VI, and remained so until 2006 when they became part of The Royal Regiment of Scotland.
During the visit, the Queen was presented with the keys to Stirling Castle before viewing a range of exhibitions on display which reflect the Highlanders' proud military history.
Exhibitions viewed by Her Majesty included Birth of a Regiment and Our Scottish Roots.
She then unveiled a plaque to formally open The Argyll and Sutherland Highlanders' Museum.
The Queen looked elegant in a fuchsia coat and matching floral hat for her engagement, and she accessorised with the Argyll and Sutherland Highlanders badge.