This book constitutes the refereed proceedings of the 20th Conference on Computabilitty in Europe, CiE 2024, held in Amsterdam, The Netherlands, during July 8-12, 2024 The 26 full papers and 2 short papers included in this book were carefully reviewed and selected from 43 submissions. This CIE 2024 focus on development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences.