Thuvia, Maid of Mars. by Edgar Rice Burroughs

Thuvia, Maid of Mars moves the focus of Burroughs' Martian series to Carthoris, the son of the human John Carter and Martian Dejah Thoris and the prince of Helium. Princess Thuvia of Ptarth and Prince Carthoris of Helium are in love. Fate, however, is against them : the princess is promised to another, the Jeddak of Kaol, Kulan Tith. So when the princess is kidnapped, suspicion falls on Carthoris, who sets out as his father would have to rescue the damsel and clear his name.
As the great airborn navies of Mars' military powers charge inexorably towards a needless war, Carthoris pursues the imperiled princess across borders and battlefields, making new enemies and allies along the way on a journey which traverses far and forgotten corners of Barsoom. Thuvia, Maid of Mars presents many familiar themes from Burroughs' books, such as damsels in distress, fantastical adventures, chivalry, and derring-do, set against a backdrop of looming war and political intrigue.
But it also introduces new elements, such as psychic armies and new flight technologies, as well as bringing entirely new races and settings to the series. It was originally published in 1916 as three serialized parts in All-Story Weekly, and published as a novel in 1920.