This book constitutes the proceedings of the 6th International Conference on Mathematical Software, ICMS 2018, held in South Bend, IN, USA, in July 2018. The 59 papers included in this volume were carefully reviewed and selected from numerous submissions. The program of the 2018 meeting consisted of 20 topical sessions, each of which providing an overview of the challenges, achievements and progress in a subeld of mathematical software research, development and use.