This is a remarkable novel. Written in 1908, it is one of the first examples of spy fiction as well as being what Wikipedia calls "one of the hidden hinges of twentieth-century writing, the place where, before our eyes, the nonsense-fantastical tradition of Lewis Carroll and Edward Lear pivots and becomes the nightmare-fantastical tradition of Kafka and Borges."
It's also a good fun story about philosophical anarchists who are trying to overthrow the world order, and a special group of philosophical police who are trying to stop them. It's about the relation between order and disorder in the world. There are quite a lot of twists in the storyline - I saw a fair few of them coming, but not all of them at all. But then, there are some bits which are dreamlike, and everything is really not as it seems...
It being G.K. Chesterton, there are some magnificently quotable quotes. Here are some of them.
We deny the snobbish English assumption that the uneducated are the dangerous criminals. We remember the Roman Emperors. We remember the great poisoning princes of the Renaissance. We say that the dangerous criminal is the educated criminal. We say that the most dangerous criminal now is the entirely lawless modern philosopher.
It may be conceded to the mathematicians that four is twice two. But two is not twice one; two is two thousand times one. That is why, in spite of a hundred disadvantages, the world will always return to monogamy.
the fear of the Professor had been the fear of the tyrannic accidents of nightmare, and how the fear of the Doctor had been the fear of the airless vacuum of science. The first was the old fear that any miracle might happen, the second the more hopeless modern fear that no miracle can ever happen.