Adam Fischer was born into a family of conductors. His father Sandor Fischer conducted the Budapest Radio Orchestra. His brother Iván, and a cousin, György, are also conductors. The Fischers lived across the street from the Budapest Opera House, and he attended his first concert at the age of five. When Haydn's "Surprise" Symphony was played, he decided to be a conductor so he could make the audience jump. He made his conducting debut at the age of 7, leading an ensemble of children playing toy instruments and singing.
He studied at the Budapest School of Music, sang in the children's choir of the Hungarian State Opera, and took the role of the Third Boy in Mozart's Magic Flute. He took higher musical studies at the Vienna State Academy, including studies with Hans Swarowsky. In 1973 he was a co-winner of the first prize in the Guido Cantelli Conducting Competition in Milan.
Fischer began his conducting career in a traditional manner, with a job as repetiteur at the Vienna State Opera. He had a major break when he took over a scheduled performance of Fidelio in Munich when Karl Böhm became ill, leading to a regular engagement to conduct the new production of Dvorák's Rusalka with Hildegard Behrens. He was principal conductor in Karlsruhe for five years, general music director of Freiburg (1981-1983), and music director of the Kassel Opera (1987-1992). While in Kassel (the site of one of Gustav Mahler's early jobs) he founded an international Gustav Mahler Festival.
He is the founder and music director of the Austro-Hungarian Haydn Orchestra, which plays in the original Esterházy Estate in the very room where Haydn premiered most of his symphonies, and has recorded Haydn's symphonies with them. He has worked in most of the major opera houses and led most of the world's great orchestras.
He now lives in Hamburg, Germany, with his wife, Doris; a daughter, Golda; and a son, Aron. In the 1990s he was surprised to meet for the first time relatives living in the United States. In 1999 he became chief conductor of the Danish Radio Sinfonietta and in the following year was named general music director of the National Theater Mannheim. He also made a successful debut conducting the Ring cycle at the Bayreuth Festival in 2001, being asked to return annually for the following three years.