Arguably the most important figure of the avant garde movement, Ornette Coleman is both revered and reviled for what he did to push jazz forward in the 60s. He developed a theory of playing he called "Harmolodics" which I still only barely understand. Ornette Coleman experimented with varying modal structures along with Paul Bley, Don Cherry, Charlie Haden and Dewey Redman, among others, years before even John Coltrane would branch into his experiments with Eastern rhythms.
Coleman would make a string of highly influential recordings in the '60s that represent the benchmark of avant garde jazz for current artists such Ken Vandermark, Branford Marsalis and even trumpeter Roy Campbell.
Among those would be The Shape Of Jazz To Come and Change Of The Century (both on Atlantic Records). Both are worth listening to if you want to learn some of the origins of avant garde. They may sound harsh and deconstructive at first listen but as you gradual into the world of Orenette and his then consistent quartet of Charlie Haden (bass), Don Cherry (trumpet) and Billy Higgins (drums) you begin to see why these two record cause such a seismic shift on the jazz scene at the time. Together they stand up as the classic albums of the jazz history.
Another album Live At The Golden Gate Vol. I & II (Blue Note) is truly essential and are a nice balance of bop and avant garde.This live date included an new trio (David Izenzon, bass; Charles Moffet, drums) that would later record slew of sensational live recordings including Live In Paris 1971. These two gig were recorded in Sweden during a European tour 1965 and captures the trio at the height of their powers. A magnificent performance that is dark but pack with technical brilliance.
If you enjoy any of these I would also recommend the following as a next purchase.
Live At The Hillcrest Club (Gambit)
Free Jazz (Atlantic)
Live In Paris 1971(Jazz Row)
Science Fiction (Columbia)
Sound Grammar (Sound Grammar)
For those looking for just the snapshot you might want look out for a compilation called Introducing to Ornette Coleman (Rhino). It only covers the Atlantic years but it does a good job of what the titles says.