Agyou Souma, the protagonist, is the IDLA Class A Detective. IDLA stands for International Detective License Agency. It's a highly respectable agency that evaluates and classifies a detective based on one's ability as a detective, from Class A to Class F. There are only 30 Class A detective in the whole world and there are only 2 Class A detective in Japan.
IDLA also collects all kinds of requests and offers them to the detectives to work on it. Its base is located in London. Of course, Souma is the type of person who most likely won't accept any cases from the IDLA.

He is a stoic, brooding man of few words, his incredible observation and deduction skills are tempered by his abysmal luck. He can't even step out for a cup of coffee without the cafe being robbed, or cross the street without walking into a firefight between two rival gangs. Still, what can he do? Life goes on...

Over the course of the game, Souma works on four separate (but simultaneous) cases, each of which contains a unique storyline that is independent of the others, and meets a vast array of characters. If he clears all four cases with time to spare, a more complex, fifth case is presented.

[From a combination of a forum post by Jeffrey and a GameFAQs review.]