Great Ballet styles article taken from Dance.net - by illuvia with help from wikipedia

Balanchine method (American ballet):

Balanchine style, named after the legendary choreographer George Balanchine, is a technique of dancing characterized by more open and emphasized lines, speedy allegros, and very little plie. In Balanchine Technique, the preparation for en-dehors pirouettes is a 4th position with a straightened back leg (the leg that becomes the working leg).



Bournonville School(Danish Ballet):

The Bournonville School is a very distinctive style of ballet, most associated with the Royal Danish Ballet and its leader for many years, August Bournonville.
The technique features very basic use of arms, usually keeping them in preparatoire position. Perpetual use of simple diagonal epaulements. Vocabulary for men is essentially varied forms of beats. Pirouettes are taken with a low developpe into seconde, then from seconde, for outside turns, and with a low developpe into 4th for inside turns. Enormous use of fifth position bras en bas (preparatory position) for beginning and ending movements. Has many recognizable poses such as pointe derriere one arm in 5th, the other a la taille (at the waist), with a touch of epaulement. Famous dancers from this school include Erik Bruhn, and most notably nowadays, Johan Kobborg.



Royal Academy of Dance (English Ballet):
The Royal Academy of Dance (RAD) was established in 1920 by a group of professional dance artists brought together by Philip Richardson, editor of the Dancing Times and including:
Adeline Genée - Denmark
Tamara Karsavina - Russia
Lucia Cormani - Italy
Edouard Espinosa - France
Phyllis Bedells - England
Representing the principal dance training methods of the time the group formed the Association of Teachers of Operatic Dancing in Great Britain. Over the next fifteen years the Association grew in size and influence and which lead to the granting of a royal charter. At the last Privy Council Meeting of King George V in 1936 the Association became the Royal Academy of Dancing.
In 1997 The Benesh Institute, international centre for Benesh Movement Notation, was amalgamated with the Royal Academy of Dancing.
With over 15,500 members in 82 countries the Royal Academy of Dance is one of the largest and most influential dance education and training organisations in the world. Members receive a monthly magazine "Dance Gazette". It is the largest classical ballet examining body in the world. Over 200,000 candidates take RAD examinations each year.
The annual Genée award has been made since 1980, for dancers aged 18 or 19, organised by the R.A.D. It is usually held in London. In 2004 gold medals were awarded to Alexander Jones and Ayako Ono. In addition gold medallists receive 7,500 Euros. Many gold and silver medallists go on to join the Royal Ballet, London.



French School(French Ballet)
The "École Française" (French school of ballet, French style), is characterized by an emphasis on precision, elegance, and sobriety.
The French are known for their complex beats, and their rigorous technical cleanliness, called "placement", which is more important to them than virtuosity.
Mega-star dancer & choreographer Rudolf Nureyev choreographed re-worked versions of the great academic classic ballets (such as "La Bayadère", "Swan Lake", "Romeo & Juliet", "Raymonda", "Cinderella", "Sleeping Beauty", & directed Paris Opera ballet. His artistic direction was extremely strong, and he formed and named a whole generation of young principals ("Étoiles"), called the Nureyev Babies. (Manuel Legris, Laurent Hilaire, Kader Belarbi, Isabelle Guerin, Elisabeth Maurin, amongst others). Since that time the French school has turned into the Nureyev school, with his very idiosyncratic style, based on all the steps that Nureyev himself excelled at. Great speed and quantity of steps, necessitating the music to be played slower are characteristic of this style. This influence lasts from the 1980's to the 2000's, when it is just starting to wane, as the Nureyev Babies retire.



Cecchetti method(Italian Ballet)
The Cecchetti method of ballet instruction was created by Enrico Cecchetti (1850-1928). The method traditionally has eight grades.
Grades one through four were added after Cecchetti died. Grades five through eight correspond to his original levels. Grades one through four are commonly seen in local studios to ready their pupils for the more advanced professional levels. If you pass level five then you are considered a real dancer. There are five different marks for passing a level. From lowest to highest they are: passed, passed plus, passed with commended, passed with highly commended, and passed with honours.
Grade five marks the beginning of the professional levels and is known as elementary level. Grade six is known as intermediate level and grade seven is known as advanced level. A student who has achieved grade seven is qualified to teach the Cecchetti Method. After finishing advanced level students can choose to go on to Diploma A and Diploma B in order to further their learning.




Vaganova method(Russian Ballet)
The Vaganova method is a method of teaching classical ballet that was founded by Agrippina Vaganova and developed into an exact science by her pedagogical pupil for over 30 years, Vera Kostrovitkaya and countless other teachers in the decades following Vaganova's death in 1951. Therefore, it is really a misnomer to call it that, as she meant for it to be called the teaching of classical dance. It is in the mistranslation of the title of her book, "Basic Principles of Russian Classical Dance" that it is implied that it is her method. She actually titled her book: "The Foundation for Dance." It is combination of the finest of the esthetics and physical results of strength, from French, Danish, and Italian schools, the method has produced many of the world's best dancers and continues to do so today. Vaganova is known for founding the Soviet System of Ballet Education, but her and Kostrovitskaya's teaching method has developed into the applied laws of physics and the core of the teaching does not need to be constantly revised and modified, as other ways of teaching that are not scientific. The method is still used worldwide.
The method demands precision in instruction, including how to teach, when to teach, how much of each exercise to give and for how long and when to change forms. Its results in addition to sound technique are a strong lower back, plasticity of the arms and the exact amount of strength, flexibility and endurance in the muscle needed to execute one of the most difficult movements known to ballet - that of the classical pas de deux. Although it is widely in use, being the most common ballet teaching method in Russia and parts of Europe, and the most popular also in the North America and other parts in the world, in today's world, few really understand fully the material. Only a few people outside of Russian Ballet Schools understand how to teach classical ballet (people don't teach the method, they teach classical ballet).