Bottazzini's research deals with the development of mathematical analysis in the 19th century, especially the work of Bernhard Riemann, Augustin-Louis Cauchy, and Karl Weierstrass. Bottazzini was the editor, with added commentary, for a new edition of Cauchy's Cours d'analyse; the new edition was published in Bologna in 1990 by CLUEB (Cooperativa Libraria Universitaria Editrice Bologna).
