Preface1 Smooth and sudden changes 1. Catastrophes 2. The Zeeman catastrophe machine 3. Gravitational catastrophe machines 4. Catastrophe theory2 Multidimensional geometry 1. Set-theoretic notation 2. Euclidean space 3. Linear transformations 4. Matrices 5. Quadratic forms 6. Two-variable cubic forms 7. Polynomial geometry3 Multidimensional calculus 1. Distance in Euclidean space 2. The derivative as tangent 3. Contours 4. Partial derivatives 5. Higher derivatives 6. Taylor series 7. Truncated algebra 8. The Inverse Function Theorem 9. The Implicit Function Theorem4 Critical points and transversality 1. Critical points 2. The Morse Lemma 3. Functions of a single variable 4. Functions of several variables 5. The Splitting Lemma 6. Structural stability 7. Manifolds 8. Transversality 9. Transversality and stability 10. Transversality for mappings 11. Codimension5 Machines revisited 1. The Zeeman machine 2. The canonical cusp catastrophe 3. Dynamics of the Zeeman machine 4. The gravitational machines 5. Formulation of a general problem6 Structural stability 1. Equivalence of families 2. Structural stabillty of families 3. Physical interpretations of structural stability 4. The Morse and Splitting Lemmas for families 5. Catastrophe geometry7 Thom's classification theorem 1. Functions and families of functions 2. One-parameter families 3. Non-transversaliity and symmetry 4. Two-parameter families 5. "Three-, four- and five-parameter families" 6. Higher catastrophes 7. Thom's theorem8 Determinacy and unfoldings 1. Determine and strong determinacy 2. One-variable jet spaces 3. Infinitesimal changes of variable 4. Weaker determinacy conditions 5. Transformations that move the origin 6. Tangency and transversality 7. Codimension and unfoldings 8. Transversality and universality 9. Strong equivalence of unfoldings 10. Numbers associated with singularities 11. Inequalities 12. Summary of results and calculation methods 13. Examples and calculations 14. Compulsory remarks on terminology9 The first seven catastrophe geometries 1. The objects of study 2. The fold catastrophe 3. The cusp catastrophe 4. The swallowtail catastrophe 5. The butterfly catastrophe 6. The elliptic umbilic 7. The hyperbolic umbilic 8. The parabolic umbilic 9. Ruled surfaces10 Stability of shipsStatic equilibrium1. Buoyancy2. Equilibrium3. Stability4. The vertical-sided ship5. Geometry of the buoyancy locus6. MetacentresShip shapes7. The elliptical ship8. The rectangular ship9. Three dimensions10. Oil-rigs11. Comparison with current methods11. The geometry of fluidsBackground on fluid mechanics1. What we are describing2. Stream functions3. Examples of flows4. Rotation5. Complex variable methodsStability and experiment6. Changes of variable7. Heuristic programme8. Experimental realizationCombining polymer molecules9. Non-Newtonian behaviour10. Extensional flowsDegenerate flows11. The six-roll mill12. The non-local bifurcation set of the elliptic umbilic13. The six-roll mill with polymer solution14. The 2n-roll mill12 Optics and scattering theoryRay optics1. Caustics2. The rainbow3. Variational principles4. ScatteringWave optics5. Asymptotic solutions of wave equations6. Oscillatory integrals7. Universal unfoldings8. Orders of causticsApplications9. Scattering from a crystal lattice10. Other caustics11. Mirages12. Sonic booms13. Giant ocean waves13 Elastic structuresGeneral theory1. Objects under stress2. Elastic equilibria3. Infinite-dimensional peculiaritiesEuler struts4. Finite element vision5. Classical (1744) variational version6. Perturbation analysis7. Modern functional analysis8. The buckling of a spring9. The pinned strutThe geometry of collapse10. Imperfection sensitivity11. "(r, s)-Stability"12. Optimization13. Symmetry: rods and shellsBuckling plates14. The von Kármán equations15. Unfolding a double eigenvalueDynamics16. Soft modes17. Stiffness14 Thermodynamics and phase transitionsEquations of state1. van der Waals' equation2. FerromagnetismThermodynamic potentials3. Entropy4. Transforming the maximum entropy principle5. Legendre transformations6. Explicit potentials7. The Landau theoryFluctuations and critical exponents8. Classical exponents9. Topological tinkering10. The rôle of fluctuations11. Spatial variation12. Partition functions   13. Renormalization group14. Structural stability of renormalizationThe rôle of symmetry15. Even functions16. The shapes of rotating stars17. Symmetry breaking18. Tricritical points19. Crystal symmetries20. Spectrum singularities15 Laser physicsPreliminaries1. Atoms2. Field3. Interaction4. MeasurementThe laser catastrophe5. Unfolded Hamiltonian6. Equations of motion7. Mean field approximation8. Boundary conditions9. Non-equilibrium stationary manifoldExperiments10. Laser transition11. Optical bistability12. Photocount distributionsAnalytic correspondence13. Equilibrium boundary conditions14. Equilibrium manifold15. Thermodynamic phase transition16. Critical behaviour17. Analytic correspondence of experiments &