Geiger was the daughter of the composer and the court hat-maker/modist Theresia Geiger (née Ržiha, 1804–1865). Her parents nurtured her musical talents, and her father was her first piano teacher. She continued piano lessons with
Johann Wenzel Tomaschek as well as
Simon Sechter. Sechter gave her lessons in composition and counterpoint as well. Geiger made her public debut as a concert pianist at age six. She played her own compositions in public first at age eight. She made her theatrical stage debut in 1852 at the
Friedrich-Wilhelm-Städtische Theater, Geiger is the first female composer ever to be featured in the Vienna Philharmonic's
Neujahrskonzert. ==Selected compositions==