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Mueller studied violin in Basel and conducting in Cincinnati, Ohio. He then became a Conducting Fellow in Tanglewood, Massachusetts, and worked with Seiji Ozawa, Robert Spano and Leon Fleisher. In 1996, Mueller was appointed assistant to Vladimir Ashkenazy at the Deutsches Symphonie-Orchester in Berlin. In 2000, Mueller won the International Conducting Competition in Cadaqués, Spain. From 2001 to 2005, he was Assistant Conductor to Claudio Abbado at the Gustav Mahler Youth Orchestra, and held the same position at the Lucerne Festival Orchestra from 2003 to 2005. During the 2004/2005 season, he was the Cairo Symphony Orchestra's Music Director. Since 2005, Christoph-Mathias Mueller is the Principal Conductor and Artistic Director of the Göttinger Symphonie Orchester, and the orchestra's General Music Director since 2007.
Beyond these functions, Mueller is frequently invited to guest-conduct internationally. In 2005/2006, he conducted the French premiere of the entire ballet “Ondine” by Hans Werner Henze at the Opéra National in Strasbourg. In 2010, he led the Bolshoi Theatre's new production of Die Fledermaus in Moscow. Further guest appearances and conducting engagements were with the BBC National Orchestra of Wales, the SWR Sinfonieorchester, the Orchestra della Svizzera Italiana, the Russian National Orchestra and with the Ensemble Modern.