• Historical Perspective.- Hyperbolic Systems: Riemann Invariants, Rarefaction Waves.- Hyperbolic Systems: Contact Discontinuities, Shocks.- The Burgers Equation and the 1-D Scalar Case.- The 1-D Scalar Case: the E-Conditions of Lax and of Oleinik.- Hopf's Formulation of the E-Condition of Oleinik.- The Burgers Equation: Special Solutions.- The Burgers Equation: Small Perturbations; the Heat Equation.- Fourier Transform; the Asymptotic Behaviour for the Heat Equation.- Radon Measures; the Law of Large Numbers.- A 1-D Model with Characteristic Speed 1/?.- A 2-D Generalization; the Perron–Frobenius Theory.- A General Finite-Dimensional Model with Characteristic Speed 1/?.- Discrete Velocity Models.- The Mimura–Nishida and the Crandall–Tartar Existence Theorems.- Systems Satisfying My Condition (S).- Asymptotic Estimates for the Broadwell and the Carleman Models.- Oscillating Solutions; the 2-D Broadwell Model.- Oscillating Solutions: the Carleman Model.- The Carleman Model: Asymptotic Behaviour.- Oscillating Solutions: the Broadwell Model.- Generalized Invariant Regions; the Varadhan Estimate.- Questioning Physics; from Classical Particles to Balance Laws.- Balance Laws; What Are Forces?.- D. Bernoulli: from Masslets and Springs to the 1-D Wave Equation.- Cauchy: from Masslets and Springs to 2-D Linearized Elasticity.- The Two-Body Problem.- The Boltzmann Equation.- The Illner–Shinbrot and the Hamdache Existence Theorems.- The Hilbert Expansion.- Compactness by Integration.- Wave Front Sets; H-Measures.- H-Measures and “Idealized Particles”.- Variants of H-Measures.- Biographical Information.- Abbreviations and Mathematical Notation.

From the reviews: "The book is well organized. ... Tartar is excellent in bringing out the essence of ideas and methods ... . The monograph is an interesting read from more than one point of view. First, the mathematically literate reader finds an extensive ... review of the relevant subjects; reading the sketches of proofs offers a bird's eye view of the underlying concepts as well as the exceptional mind of the author. ... All in all, a remarkable book." (Reinhard Illner, SIAM Reviews, Vol. 51 (2), June, 2009) "This is a very nice book devoted to hyperbolic systems of conservation laws. ... This book can be recommended to all researchers in respective areas, especially to graduate students."--- (Mitsuru Yamazaki, Mathematical Reviews, Issue 2010 j)