Answer:
Bebop ---- small groups using complex harmonies
Cool jazz ---- relaxed style of jazz popular around the late 40s and 50s
New Orleans jazz ----- introduced group improvisation
Swing ----- big band music
Bebop was born in the mid-1940s and is characterized by small groups that play complex musical structures. Its musicians experiment with faster tempos and complex chord progressions. One reason for its freedom to experiment is that is not a style focused on dancing.
Cool jazz was born in the late 1940s and 1950s. It is a lighter and more romantic style of jazz. It was born from the migration of musicians from California to New York. In the 1950s Miles Davis took an interest in it and produced his album Kind of Blue (1959).
New Orleans jazz is the starting point of the history of jazz. It was born with this name between 1890 and 1910 in black communities from music played by African-Americans.
The swing was a popular style in the 1930s and 1940s for dancing. It was played by big bands (ten or more musicians). It frequently had musicians that would solo on the melody over the arrangement.
