http://en.wikipedia.org/wiki/Jean-luc_Godard
"Many of Godard's films challenge the conventions of traditional Hollywood cinema as well as the French equivalent, namely the "tradition of quality". He is often considered the most extreme or radical of the New Wave filmmakers. His films express his political ideologies as well as his knowledge of film history. In addition, Godard's films often cite existential and Marxist philosophy."
Most find his only notable period to be between Breathless (1959) and Week End (1967). But that 9-year period is seen as essential French New Wave cinema. From wikipedia: "
Week Ends' enigmatic and audacious end title sequence, which reads "End of Cinema", appropriately marked an end to the narrative and cinematic period in Godard's filmmaking career." (He is still making films, though I know of no one who sees them, even in the art house circles. He also works more often in short length format now rather than feature length, and often on video rather than film).
Personally speaking, I think both Breathless and Week End are great films. The former is more in line with what people think of as French New Wave, and is my personal favorite from Godard (I would rank it slightly below Truffaut's The 400 Blows). The latter.... well, its usually as far as people go with Godard in his filmmaking journey, and can be quit divisive. I love its boldness and blatantly radical politics.
I wasn't a big fan of Contempt (1963) or Pierrot le fou (1965), but they were both interesting and worth watching. His other notable films of this era that I have yet to see include Vivre sa vie (1962), Band of Outsiders (1964), A Woman is a Woman (1961), Alphaville (1965), and Masculine Feminine (1966), all released by Criterion.