This is part of the Eye on I season at the ICA. All four films are essential viewing. Details here.
Chicago Reader review of Alphaville:
The unadorned streets of Paris become Alpha 60, Capital of Pain, in Jean-Luc Godard's smoky, acrid 1965 science fiction film. It's the most political of Godard's films before his complete radicalization, and probably his most anguished. The terrain crossed by special agent Lemmy Caution (B movie star Eddie Constantine) is relentlessly sterile and oppressive, a wilderness of glass-box architecture and endless white corridors. The view of technology as inherently evil is too facile for Godard's fine, paradoxical mind, and the film as a whole is light on insight. But it remains an outstanding example of the filmmaker's power to transform an environment through the selection of detail: everything in it is familiar, but nothing is recognizable. With Anna Karina and Akim Tamiroff.
Here (and above) is the trailer.
Here is academic Colin MacCabe's introduction to Alphaville.