Ch. 1. Introduction -- ch. 2. Historical background. 2.1. The early history of accelerators. 2.2. Accelerator physics in the Midwest. 2.3. The coming of strong focusing. 2.4. The desire for a new accelerator laboratory in the Midwest -- ch. 3. The early MURA years, 1953-1956. 3.1. The beginnings of MURA. 3.2. The invention of FFAG. 3.3. MURA studies. 3.4. Theory of radio frequency acceleration. 3.5. Nonlinear dynamics. 3.6. The radial sector model. 3.7. The spiral sector model. 3.8. MURA computing. 3.9. Colliding beams. 3.10. Collective instabilities. 3.11. Conferences -- ch. 4. The Madison years, 1956-1963. 4.1. Formation of the MURA organization. 4.2. The move to Madison. 4.3. Space charge. 4.4. Injection and extraction. 4.5. The 50 MeV two-way model. 4.6. MURA proposals. 4.7. The 1959 workshop; synchrotrons catch up. 4.8. The directorship of Bernard Waldman. 4.9. The panel and their recommendations. 4.10. MURA responds -- ch. 5. The last years of MURA, 1963-1967. 5.1. The end of MURA. 5.2. The ZGS tuneup and improvement program. 5.3. Linacs. 5.4. Magnet development. 5.5. Cosmic rays. 5.6. Bubble chambers. 5.7. The electron storage ring. 5.8. The physical sciences laboratory; the synchrotron radiation center. 5.9. Fermilab. 5.10. Cyclotrons and nonscaling FFAGs today and tomorrow. 5.11. MURA's last gasp -- ch. 6. Consequences and reflections. 6.1. Innovations. 6.2. Innovation was not enough. 6.3. Personal note