Galeazzi was born in Chiari (Brescia), Italy and studied at "La Scala", Milan, where she earned her diploma with honors. She joined the Royal Ballet in 1992 and was promoted to First Artist in 1995, Soloist at the end of the 1997/98 Season and Principal in September 2003. She retired from the Royal Ballet in June 2013.  In addition to her work with The Royal Ballet, Galeazzi frequently appeared as a guest artist with other ballet companies around the world including the Stuttgart Ballet, the Scottish Ballet, the South African Ballet Theatre, and the Cape Town City Ballet. She has also performed with such notable dancers as Irek Mukhamedov, Carlos Acosta, and Tetsuya Kumakawa. She performed with the Opera di Roma the new production of Le Corsare and Carla Fracci Giselle .
Within the classical repertory, Galeazzi has performed such roles as the title role in Fokine's The Firebird, the Sugarplum Fairy in Tchaikovsky's The Nutcracker, the title role in Adolphe Adam's Giselle, Gamzatti in Natalia Makarova’s production of La Bayadère, the title role in Edouard Deldevez's Paquita, and the Bluebird in Tchaikovsky's The Sleeping Beauty to name just a few.
She is also known for her performances of more contemporary pieces, especially the works of Frederick Ashton, Kenneth MacMillan, Twyla Tharp, Wayne McGregor, Glen Tetley, Christopher Wheeldon, Alastair Marriott,and Ashely Page.
Her television performances have included a live BBC broadcast from The Royal Opera House when she danced Aurora in Ninette de Valois’ Coppélia (February 2002), Ashton’s Thais pdd (November 2004), Voices of spring (April 2005) and Sylvia (December 2005). Her performance of Symphony in C was broadcast live in many big squares all over the UK in June 2005. The director Philip Cox produced the documentary Facing Mara.
Galeazzi has been actively involved in several charitable outreaches. In 2005 she organized a charity gala which raised money to help children with leukemia. The success of this gala led her to start the organization Dancing for the Children which focuses on raising money to help children effected by the AIDS epidemic in Africa.
Honors and awards
- In November 2003 she received the nomination as Best Female Dancer at Critics’ Circle National Dance Award.
- In February 2005, after a Charity Gala in her home town of Brescia, Mara became an honorary member of Soroptimist International, a worldwide organization for women in management and the professions aimed at equality, development and peace.
- In May 2006 she is appointed 'Best Italian Dancer Abroad' (Danza & Danza Award).
- In March 2009 she was given the medal of "CAVALIERE DEL LAVORO" (KNIGHTHOOD) from the Italian president Giorgio Napolitano
In 2011 to see Galeazzi dance Elite Syncopations in the MacMillan triple bill [The Royal Ballet] out on DVD
In 2011 to see Galeazzi dance in Chroma, Limen, Infra for Wayne McGregor [The Royal Ballet] out on DVD