The first of the Death books. Death appeared before, but this is the one where he's a major character, and takes on his final personality. (You may be surprised if you only read the earlier ones.)
Young Mort is hopelessly clumsy and curious, and his father finally tries to get rid of him at a hiring fair. Boys all about him are taken on as apprentices, but not Mort. When midnight strikes, he tells his father it's not over until the last stroke -- and during the strokes, Death arrives. His father thinks he's being apprenticed to be an undertaker, but Mort realizes it's Death.
Death's home is noticeably black, with a bone and skull theme, and somewhat clueless. it also features a servant, Alfred, and a daughter, Ysabell. Adopted, unsurprisingly. She's the one who explains that he tries, but just doesn't get humanity.
But Death trains him. Only a few lives require Death to appear in person, but these include a royal assassination. Mort's attempt at interfering only leads to a kindly rebuke that there is no justice, just him, and mercy is a sharp blade. Then he sends Mort out on his own. Things go wrong.
This involves a coronation, a princess pulling the Death card three time from a deck with only one, the self-writing biographies in Death's library, Mort's taking an afternoon off, Death's skills as a cook, Mort walking through things only when he doesn't realize it, and much more.