The square notes are pneumes, and the clefs are "C" clefs: at the far left, you'll see what looks like a small bracket next to one of the lines on the clef. That bracket denotes the location of middle C on the staff. The lower the position of the bracket (or location of middle C), the higher the tessitura (median pitch); the higher the position of the bracket denoting middle C, the lower the tessitura.
This was the standard musical notation from about 850 CE until the late 1400s; the music system we're used to with quarter notes, half notes, brackets, treble and bass clefs began developing during the Ars Nova in mid to late 14th century motets and secular music (you should hear some of this: it's more reminiscent of Igor Stravinsky and Paul Hindemith!) and became standardized by the early 16th century.
