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This should be a very worthwhile screening series that I certainly plan to investigate throughout its run.
I’d say that the 2 most well-known Brazilian movie franchises outside of Brazil, are City of God and, more recently, Elite Squad (I & II) – both based on conflict between drug dealers, corrupt cops & politicians in the slums of Rio de Janeiro; both quite violent, but based on what was not that long ago, a cruel reality. And they’e also great movies that deserve to be watched, if you haven’t seen them yet.
The Brazilian movie industry, after decades in search of itself, seemed to explode on the international scene during the 1990s when favela-themed stories started to become filmmaker favorites, highlighting decades of social injustice within the country, and exposing to international audiences.
In the 1950s, a radical shift occurred in Brazilian cinema that saw the introduction of techniques popular within the Italian Neorealism movement, which ignited the Cinema Novo (New Cinema) movement that rose to prominence in Latin America during the 1960s and 1970s, emphasizing social equality and intellectualism, eschewing traditional Hollywood filmmaking.
In the 1960s the Tropicália movement took over Brazil – an artistic movement (film, music, theatre and other kinds of art) whose universal goal was to channel all foreign influence into creating unique national products. Around the same time, in the late 1960s, Cinema Marginal was also taking hold in Sao Paulo and Rio de Janeiro, which saw directors focus on the marginalized in society. At the time, the country was run by a repressive military dictatorship, leaving behind a burgeoning leftist culture. Faced with an artistically oppressive state, a group of young underground filmmakers, turned to cinema as a tool for political resistance, as well as self-investigation. 
As artist and filmmaker Lygia Pape stated, “Marginal was the revolutionary act of invention, a new reality, the world as change, error as adventure and the discovery of freedom…the anti-film.
Some of those “anti-films” are included in New York’s Museum of Modern Arts’ (MoMA’s) series, On the Edge: Brazilian Film Experiments of the 1960s and Early 1970s, which charts the era’s vibrant underground cinema scene.
Running from May 10–July 24, 2014, some of the sections and individual titles (shorts and features) included in the series are: 
Apocalipopótese and After – Friday, May 16, 2014, 7:00 p.m., Theater 2, T2

Artistic experimentation in Rio during the 1960s culminated in the collective exhibition Apocalipopótese, in Rio’s Atero do Flamengo park. Documented in beautiful 16mm by the marginal poet Raymundo Amado, the exhibition included Lygia Pape’s Ovos (Eggs), cloth boxes from which an enclosed person breaks forth; Antonio Manuel’s Urnas quentes, wooden boxes that participants broke open to reveal slogans like “Down with the Dictatorship” and “Power to the People”; and poet Torquato Neto and critic Frederico Morais donning Oiticica’s Parangolécapes. The exhibition marked the passage from the 1960s to the 1970s in the work of the group of artists around Clark and Oiticica.

Apocalipopótese 

1968. Brazil. Directed by Raymundo Amado. 9 min.

Cinemateca-Rio 

1963. Brazil. Directed by Lygia Pape. 1 min.

Hermetic Triumph 

1972. Brazil. Directed by Rubens Gerchman. 12 min.

Semi Ótica 

1975. Brazil. Directed by Antonio Manuel. 7 min.

Agripina é Roma-Manhattan 

1972. USA. Directed by Hélio Oiticica. 15 min.

HO 

1979. Brazil. Directed by Ivan Cardoso. 13 min.

And in the features section are, Glauber Rocha’s Deus e o diabo na terra do sol (Black God, White Devil, 1964):
The great Cinema Novo movement’s leading light was Glauber Rocha, whose manifesto, “Aesthetics of Hunger,” and passion for finding a cinematic language capable of reflecting the country’s tremendous social and human problems was frequently discussed in the circle of artists around Lygia Clark (an alternative artistic milieu of which Rocha was also a part). The film is the frenzied parable of a peasant who has killed his master and seeks help first from a holy man and later from a cangaceiro (a peasant “social bandit” of northeastern Brazil). It is inspired by Brazilian—mostly black—theatrical tradition, but the poetic, almost baroque, style is Rocha’s personal signature. In Portuguese; English subtitles. 125 min.
And Arthur Omar’s Triste trópico (1974):
In this “fake documentary” a doctor returns to Brazil after studies in Paris. Setting out to practice medicine, he becomes an indigenous messiah and, in time, a cannibal. Omar’s cinema distinguishes itself from both the aesthetics of Cinema Novo and Marginal Cinema’s extreme photographic realism by what he has called a “hyper-language,” a collage constructed with many kinds of images, printed words, letters, drawings, symbols, documentary material, archives of family films, snapshots, and, in the voice-over, dozens of texts from anthropological research, baroque narratives, popular almanacs, sermons, poems, and citations of all sorts—all set off with a purposeful and radical lack of perfection in its overall visual look. In Portuguese; English subtitles. 80 min.
The screening series is being presented in conjunction with the exhibition Lygia Clark: The Abandonment of Art, 1948–1988, by the Department of Film.
Full details, including complete lineup, can be found HERE.