Rock & Roll
Rock & Roll emerged in the early fifties, eventually becoming the genre Rock Music. Rock was primarily influenced by blues, and country music, with some elements of gospel. The word was coined by Alan Freed, a Cleveland disk jockey. Originally an American invention, Rock has given birth to numerous styles on several continents.
Blues
Blues is a genre of music related to Jazz. From a theory perspective most blues uses jazz chords but with a different progression. Also a distinctive culture has grown up around blues music. Blues has its origins in folk music, as well as lyrical influences going back to African American folk music of the post slavery era.
Country
Country music evolved from several styles including Celtic, Folk, gospel, and ethnic southwestern music. Western themes, and acoustic guitars often characterize country.
Jazz
Jazz came about by combining both European and African music traditions. Jazz popularly includes syncopation, and improvisation. Jazz has influenced several other genres and remains a popular format today.
Roots
Root music incorporates aspects of folk, blues, and country. It is a genre similar to folk, or folk revival. Where as folk revival seeks to restrict itself to folk music traditions, roots is more all encompassing, and has a larger array of music styles and instruments.