My first thought was to do it by decade, to which I pulled together the following syllabus. I'd start with the more modern films as they'd be more accessible and gradually move backwards.

I've tried to cover off most of the essential directors, most of the essential movements, and where possible, films that were particularly important for the time they were released. Obviously not perfect but I think it's a pretty good overview.

2010s - Her, Boyhood, The Tree Of Life, The Social Network, Under The Skin

2000s - In The Mood For Love, Werckmeister Harmonies, Synecdoche New York, Lost In Translation, Spirited Away

1990s - Magnolia, Three Colours Blue, The Big Lebowski, Rushmore, American Beauty

1980s - Damnation, Do The RIght Thing, The Evil Dead, Withnail And I, Blue Velvet

1970s - Stalker, Aguirre Wrath Of God, Badlands, Apocalypse Now, Chinatown

1960s - 2001: A Space Odyssey, Le Mepris, 8 1/2, Persona, La Notte

1950s - Vertigo, Tokyo Story, The 400 Blows, Rashomon, The Night Of The Hunter

1940s - Citizen Kane, The Maltese Falcon, It's A Wonderful Life, Casablanca, The Red Shoes

1930s - The Rules Of The Game, City Lights, Gone With The End, Bringing Up Baby, L'Atlante

1920s - The Cabinet Of Dr. Caligari, Man With A Movie Camera, The General, The Passion Of Joan Of Arc, Metropolis