Fritz Lang's first sound picture is also, as far as I know, the first instance of the serial-killer sub-genre. It is a beautifully-composed film benefiting from the exclusively visual medium of silent cinema whilst also acquiring the more naturalistic effects of sound. Some of the characteristic devices of German Expressionist cinema, particularly the extreme angle of shots and the chiaroscuro compositions, are carried over whilst developing the potential of off-screen sound and mobile camera work to create the effect of menace appropriate to the story which is no mere thriller but also a work of sociological and psychological observation
Peter Lorre, in the role that introduced him to Hollywood, is impressive as the killer, the climatic scene where he is brought before a people's court is outstanding, albeit rather histrionic by today's standards.
FYI: Lang fled Germany in 1933, leaving behind his pro-Nazi wife, Thea von Harbou, who co-wrote this and worked on all of his films in the 1920s and '30s, including his 1927 masterpiece Metropolis.
The original film was 117 minutes and now exists in various truncated versions most of which run under 100 minutes. The print used for this transfer is claimed to be the "Longest Available Version". There is also a 105 minute print restored by the Munich Film Archives and released in the late '90s (from memory a version I saw some years ago has M dying under the wheels of a truck whilst escaping his pursuers).