Kate is spending the day in The Hague and Rotterdam, where her itinerary covers a range of events from a visit to an art exhibition of Old Masters to a round-table discussion on a variety of themes from addiction to mental health.
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The one-day trip is a royal milestone for the Duchess as she will be travelling abroad by herself without the Duke.
A tour of Malta in 2014 was scheduled to be Kate's first solo trip but she had to cancel as she was suffering from acute morning sickness while pregnant with Princess Charlotte.
Kate will meet King Willem-Alexander at Villa Eikenhorst, the royal residence he shares with wife Queen Maxima and their three daughters, Princesses Amalia, Alexia and Ariane.
The family home is on the forested De Horsten estate in Wassenaar, near The Hague, and, despite being a private residence, the Dutch monarch sometimes hosts foreign guests.
Art is an interest of the Duchess, who is patron of the National Portrait Gallery, and she will visit the Mauritshuis art museum in The Hague to see an exhibition featuring Dutch Old Masters loaned by the Royal Collection, with artwork, furniture and other objects accumulated over centuries by the British monarchy.
The highlight will be Vermeer's The Music Lesson, which Kate will see after touring the gallery's permanent collection.
Before leaving, the Duchess will meet children taking part in the gallery's learning programme and attend a short reception with museum supporters.
At the official residence of Sir Geoffrey Adams, Britain's Ambassador to the Netherlands, Kate will convene a round-table discussion on the themes of addiction, intervention, family and mental health.
Taking part will be professionals from the Trimbos Institute, a non-profit research centre working on the issues of mental health and addiction.
They will be joined by counterparts from two of the Duchess's UK charities - the Anna Freud Centre for Children and Families, a leading charity in the research, teaching and the provision of care for children and young people with mental health issues, and Action on Addiction.
Later Kate will travel to the neighbouring city of Rotterdam to learn about a community initiative that provides a public workshop in an economically deprived district, with facilities aimed at teenagers.
Residents pay by sharing their skills with others, providing education, skills and positive role models in the neighbourhood.