The Vaganova style of ballet is also called Russian ballet. It is named after Agrippina Vaganova; she was a Russian ballet teacher during the early 20th century. A type of classical ballet, it is characterized by the continual flow of body movement, with soft, clean lines and a lack of the stiffness that may be apparent in other types of ballet.
The Cecchetti method of ballet was developed by Italian dancing master Enrico Cecchetti. It is marked by rigid training that focuses on the basics of classical ballet. This method presents ballet as science that can be learned, with an emphasis on clean lines and precise movements rather than graceful flourishes.
The Royal Academy of Dancing is an international cooperative that trains dancers to be well-rounded. It combines elements of both the Cecchetti and Vaganova methods and is also called the English method. It is characterized by attention to minute basic training with consistently improving technique.
Though the various classical methods are the most prominent, there are modern styles of ballet that do not adhere so strictly to the classical ballet rules. One such style is Balanchine, also referred to as neoclassical, which uses the vocabulary and basic components of classical ballet, but allows dancers to perform more technical moves dancing at faster tempos. Another modern style of ballet is generally referred to as contemporary ballet, which combines elements of ballet and modern dance. It doesn't require the strict turnout or languid body lines of classical ballet.