This volume is based on lectures presented at a colloquium held in Geneva in 2003 to honour the 200th anniversary of the birth of Charles François Sturm in Geneva on September 29, 1803. The focus is on C.F. Sturm's own work and this is the first monograph on his collected papers. These original papers are accompanied by contributions from internationally renowned experts thereby deepening topics like differential equations, optics and algebraic curves.