Princess Ingrid Alexandra pictured for the first time since returning to Norway during break from university in Australia

Princess Ingrid Alexandra is back in Norway after completing her end of semester exams in Australia.

The 21-year-old returned to her homeland in late November and she'll remain there until early next year before class resumes at the University of Sydney, where she is now a full-time student.

Rather than resting during her time off from university, the second-in-line to Norway's throne has thrown herself back into royal duties.

So far she has eight official engagements in her diary throughout December and the first was alongside her father, Crown Prince Haakon.

The father and daughter joined the Institute of Marine Research on a voyage through the Oslo fjord, aboard the research ship named Princess Ingrid Alexandria, to monitor the waterway's sprat population.

Sprats are one of the most important small fish in the Oslofjord, both as food for larger fish and seabirds, and as an indicator of how life in the fjord is developing, the palace said.

Tomorrow, the princess will visit the Directorate for Space Activities in Oslo before holding audiences inside the Royal Palace.

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On December 10, she will visit the Save the Children's Peace Prize celebration outside the Nobel Peace Centre in Oslo.

But more significantly, Princess Ingrid Alexandra will attend the Nobel Peace Prize awards for the for the first time, later that day.

The awarding of the peace prize is held in Oslo and the day after the rest of the Nobel awards take place in Stockholm, attended by Sweden's royal family.

Princess Ingrid Alexandra will attend the event inside Oslo City Hall alongside her grandparents King Harald and Queen Sonja and her parents, Crown Prince Haakon and Crown Princess Mette-Marit.

The Nobel Peace Prize will this year be presented to Venezuela's opposition leader María Corina Machado.

A banquet will be held inside Oslo's Royal Palace after the presentation of the award, but only Crown Prince Haakon will represent the royal family.

In comparison, the Swedish royals wear their finest outfits and tiaras first to the ceremony and then the banquet. The following day, another gala is held at Stockholm's Royal Palace.

This year, Princess Sofia will be absent from the celebrations as she remains on maternity leave.

On December 16, Princess Ingrid Alexandra and her younger brother Prince Sverre Magnus will host a Christmas event inside the palace chapel alongside their parents to thank the country's emergency services.

Three days later, the Crown Prince family and the King and Queen will host a Christmas lunch for the government.

Princess Ingrid Alexandra's presence at the Nobel Peace Prize awards is expected to be one of her most high-profile to date.

Despite her place as heir-in-waiting, she only begun carrying out regular appearances at public events in Norway in April.

The Norwegian royal family will come under intense scrutiny in the coming months as the stepson of the future King faces trial on charges of rape and assault.

The criminal trial against Marius Borg Høiby will begin on February 3 next year and run until March 13, in Oslo's District Court.

Last year, Høiby – the 28-year-old son of Crown Princess Mette-Marit and stepson of the heir to the throne, Crown Prince Haakon – was arrested.

He is accused of 32 crimes including domestic abuse and rape, most of which he denies, and faces 10 years in prison if convicted.

While the King and his wife Queen Sonja, who are both 88, are not expected to attend the proceedings, the Crown Prince couple are likely to be there.

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