Ballet- is a classical dance form demanding grace and precision and employing formalized steps and gestures set in intricate, flowing patterns to create expression through movement.
Jazz- dance combines techniques of classical ballet and modern dance with the current forms of popular dance. Jazz also has its own movement vocabulary ranging from the isolation of certain body parts to the movement of the entire body with the accents of musical rhythms. Jazz dance can take on many different characteristics and styles, including Street Jazz, Percussive, Broadway, Contemporary and Lyrical. Jazz classes can be patterned in any of these styles or a combination of them. Emphasis is on the importance of energy, rhythmical accuracy, and style.
Lyrical dance is a slow, expressive type of dance that incorporates ballet technique. This dance style’s main goal is to interpret the lyrics of the song through movement. 
Hip-Hop dance refers to street dance styles primarily performed to hip-hop music or that have evolved as part of hip-hop culture.