I'll Teach You A Lesson You'll Never Forget!: The Diary of a Tomboy Princess

Lana, princess of the kingdom of Mitronia, is bright and energetic with excellent swordsmanship and academic ability. A stark contrast to her older brother Adrian, the self-centered and pompous crown prince. However, he is the one scheduled to take over the throne from their father as King of Mitronia next summer.
Fearing for the future of her country, Lana vows to replace her brother as queen...! Unfortunately, this is impossible under the current law, which states that "only males in the direct line can succeed to the throne". The current king, troubled by her unprecedented proposal, tells Lana that in order for her to gain his approval, she must "solve the problems of three noble families" throughout their kingdom. Lana immediately sets out for the lands in question, accompanied by four friends, including her childhood friend, the knight Kaiser...
The tomboy princess' exhilarating journey starts here!

(Source: MangaPlaza)