The Innocence of Father Brown is the first of five collections of mystery stories featuring Chesterton's canny priest. It's probably the best collection and it introduces the holy detective—as well as his sometime opponent, sometime collaborator, Flambeau. But each collection offers some great stories.
I'm very fond of Father Brown—despite several potential obstacles.
For one thing, the plots of these stories are implausible. They are part of the tradition of British murder mysteries that the later American hardboiled school revolted against. Murders are carried out in ridiculously complicated fashions, as no crimes are committed in the real world.
Father Brown is the prototype of the intuitive amateur sleuth (like Agatha Christie's Miss Marple and TV's Jessica Fletcher on Murder, She Wrote), who runs into murders everywhere he goes and manages to solve the crimes with only one or two clues where thorough, professional investigators are stumped.
The mysteries are extremely clever on the most superficial level, with several innovations on the classic locked-door mystery and other more novel situations. But on top of that, they involve an understanding of human nature—or at least of how human nature operates in society.
Typically, Father Brown solves crimes by sharing the perpetrators' own insights into human perception, which allow them to commit the deeds and him to uncover them. He sees what others, including the readers, do not, even when it is right before our eyes.
Not always though. In about a third of the stories I did see the solution coming from a long way off. I suspect though this is because these stories, like the mysteries of Arthur Conan Doyle and Edgar Allen Poe, have become embedded in our culture. The surprise has worn off because the tricks have been replayed so many times in stories, movies and television shows since they were invented by these masters.