The last lecture course that Nobel Prize winner Richard P. Feynman gave at Caltech from 1983 to 1986 was not on physics but on computer science. The first edition of the Feynman Lectures on Computation published in 1996 and provided an overview of standard and not-so-standard topics in computer science given in Feynman's inimitable style. Although now over 20 years old, most of the material is still relevant and interesting, and Feynman's unique philosophy of learning and discovery shines through. For this new edition, Tony Hey has updated the lectures with an invited chapter from Professor John Preskill on "Quantum Computing 40 Years Later." This contribution captures the progress made towards building a quantum computer since Feynman's original suggestions in 1981. The last 25 years have also seen the "Moore's Law" roadmap for the IT industry coming to an end. To reflect this transition, John Shalf, Senior Scientist at Lawrence Berkeley National Laboratory, has contributed a chapter on "The Future of Computing Beyond Moore's Law." The final update for this edition captures Feynman's interest in Artificial Intelligence and Artificial Neural Networks. Eric Mjolsness, now a professor of Computer Science at the University of California Irvine, was a Teaching Assistant for Feynman's original lecture course and his research interests are now in the application of Artificial Intelligence and Machine Learning for multi-scale science. He has contributed a chapter on "Feynman on Artificial Intelligence and Machine Learning" that captures the early discussions with Feynman and also looks towards future developments.This exciting and important work provides key reading for students and scholars in the fields of computer science and computational physics.