Computing, today more than ever before, is a multi-faceted discipline which collates several methodologies, areas of interest and approaches: mathematics, engineering, programming, applications. Given its enormous impact on everyday life, it is essential that its debated origins are understood, and that its different foundations are explained. On the Foundation of Computing offers a comprehensive and critical overview of the birth and evolution of computing, and analyses some of the most important technical results and philosophical problems of the discipline, combining both historical and systematic analyses. The debates this text surveys are among the latest and most urgent: the crisis of foundations in mathematics and the birth of the Decision Problem, the nature of algorithms, the debates on computational artefacts and malfunctioning, and the analysis of computational artefacts as computational experiments. By covering these topics, On the Foundation of Computing provides a much needed resource to contextualise the foundational issues. For practitioners, researchers and students alike, a historical and philosophical approach such as what this volume offers becomes essential to understand the past of the discipline, and to figure out the challenges of the future. 1. Introduction 2. A fundamental Crisis 3. Computing and Deciding 4. What is Computable? 5. Mechanical Computation 6. On the Nature of Algorithms 7. Computing as a Mathematical Discipline 8. The First Generation of Computers 9. The Laws of Evolution 10. Properties of Implemented Computations 11. Specification and Implementation 12. Computing as an Engineering Discipline 13. Elements of Experimental Computing 14. Models and Simulations 15. Formal Relations 16. Computing as an Experimental Discipline 17. Conclusions Giuseppe Primiero is Associate Professor of Logic at the Department of Philosophy, University of Milan (Italy). He acts as President of the DHST Commission for the History and Philosophy of Computing (HaPoC) and Secretary General of the Association Computability in Europe (CiE). His research interests are primarily in Logic and Computation, Philosophy of Computing and Information.