The Insidious Dr. Fu-Manchu (also called The Mystery of Dr. Fu-Manchu) is based around the attempts of Denis Nayland Smith, a police commissioner from what was then Burma who has been given a roving commission in an attempt to hunt down Dr. Fu-Manchu, and his colleague Dr. Petrie. The duo are similar to Holmes and Watson, with Petrie writing down the narrative, although Smith lacks Holmes' brilliance, mostly possessing a sheer doggedness in his actions.
The book starts when Smith appears in Dr. Petrie's house in England, even though Petrie thought Smith was in Burma at the time. Smith explains that he is hunting down an evil genius, Dr. Fu-Manchu, who has been assassinating Westerners considered to be inimical to the plans of Fu-Manchu and those he is working on behalf of. Fu-Manchu does not use guns and explosives, but a variety of poisons and assassins to do his bidding. Deaths in the story are from means that are often not obvious, sometimes considered natural causes or suicide, and that have to be fathomed out by the pair.
The duo track Fu-Manchu's murderous path across London and England, enjoying some success, but frequently being a step behind. A slave girl of Fu-Manchu does, for some reason (in the book largely put down to her being Eastern), become infatuated with Dr. Petrie and, although still working for Fu-Manchu, helps them out from time to time, especially when doing so will save Petrie's life.
What does unfortunately let the book down is the inherent racism in it. Dr. Fu-Manchu is said to be the Yellow Peril (the term for the believed way in which the Oriental countries were assaulting the West) personified, and the story is to some extent based on the idea that the yellow race (the book's terms) is attacking the white race. Fu-Manchu is acting on behalf of the yellow race and Smith is the defender of the white race. Fu-Manchu's evil is considered to be at least partly from his being Chinese. The book was written in 1911.
If you are of Chinese descent, you are likely to justifiably find parts of the book massively offensive, and even if you aren't, you are still quite likely to find the same parts distasteful. A shame, really, as otherwise The Insidious Dr. Fu-Manchu would be more enjoyable if Fu-Manchu was behaving like a normal megalomaniac.