Preface; 1. Introduction; Part I. Gasdynamics Review: 2. Governing equations of gasdynamics; 3. Waves; 4. Scalar conservation laws; 5. The Riemann problem; Part II. Computational Review: 6. Numerical error; 7. Orthogonal functions; 8. Interpolation; 9. Piecewise-polynomial reconstruction; 10. Numerical calculus; Part III. Basic Principles of Computational Gasdynamics: 11. Conservation and other basic principles; 12. The CFL condition; 13. Upwind and adaptive stencils; 14. Artificial viscosity; 15. Linear stability; 16. Non-linear stability; Part IV. Basic Methods of Computational Gasdynamics: 17. Basic numerical methods for scalar conservation laws; 18. Basic numerical methods for the Euler equations; 19. Boundary treatments; Part V. Advanced Methods of Computational Gasdynamics: 20. Flux averaging I: flux-limited methods; 21. Flux averaging II: flux-corrected methods; 22. Flux averaging III: self-adjusting hybrid methods; 23. Solution averaging: reconstruction-evolution methods; 24. A brief introduction to multi-dimensions; Index.