Throne of glass by sarah j.maas

An alternate cover edition can be found here.

After serving out a year of hard labor in the salt mines of Endovier for her crimes, 18-year-old assassin Celaena Sardothien is dragged before the Crown Prince. Prince Dorian offers her her freedom on one condition: she must act as his champion in a competition to find a new royal assassin.

Her opponents are men-thieves and assassins and warriors from across the empire, each sponsored by a member of the king's council. If she beats her opponents in a series of eliminations, she'll serve the kingdom for four years and then be granted her freedom. Celaena finds her training sessions with the captain of the guard, Westfall, challenging and exhilirating. But she's bored stiff by court life. Things get a little more interesting when the prince starts to show interest in her... but it's the gruff Captain Westfall who seems to understand her best.

Then one of the other contestants turns up dead... quickly followed by another. Can Celaena figure out who the killer is before she becomes a victim? As the young assassin investigates, her search leads her to discover a greater destiny than she could possibly have imagined.