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Contence Prologue. A Bouncing Ball 1. Hertz Contact Problem 2. Impact 3. Sticking to Plane 4. Energy Losses 5. Duration of Bouncing Tale 1. Pendulum and WKB Approximation 1. Adiabatic Pendulum 2. Precision of Adiabatic Invariant Conservation 3. Connected Pendulums Tale 2. Waves on Shallow Water 1. KdV Equation 2. The Inverse Scattering Problem for Schroedinger Equation and on Solutions of KdV 3. Solitons and their collisions 4. Appendix. Solitons. 1 Tale 3. Supersymmetry or how to get a Square Root from an Operator 1. Supersymmetry and Witten's Supersymmetric Mechanics. 2. A life case 3. Reectionless Potential Tale 4. A Drunkard and Policemen Tale 5. Dirac Monopole, a Quantum Top and Macroscopic Spin Tunneling Tale 6. Kramers' Phase 1. A paradox with Balmer Formula 2. Laplace Method and a Regular Turning Point 3. Kramers' Phase for the Coulomb Potential. Tale 7. Singularities and their Classication Tale 8. Taylor Instability and Ship Waves 1. The Taylor Instability 2. Circles on the Water formed by a falling Stone 3. Trace of a Moving Boat. 2 Tale 9. Hidden Symmetry of the Kepler Problem 1. Puzzle of Closed Orbits. 2. Fock's Sphere 3. Angular Momentum and Runge-Lentz Vector 4. Quntum Mechanics, Energy Levels, Accidental Degeneracy and Wave Functions. 5. Appendix 1. Parabolic Coordinates 6. Appendix 2. Continuum, Fock's Hyperboloid, O(2; 1) Algebra and Eigenstates of Continuum 7. Appendix 3. Zero Energy. Tale 10. Rates of Activation Processes, the Kramers' problem of Escape from a Trap and the Wiener-Hopf Method 1. Kramers' Problem 2. Two Kramers' regimes 3. Crossover between Regimes. Integral Equation. 4. Wiener-Hopf Method for Solution of Integral Equations Tale 11. Collapse of a Bubble in the Water, Scaling and the Qualitative Theory of Dierential Equations 1. Rayleigh Problem of Collapsing Bubbles. 3 2. Compressibility and Self-similar Solutions of Partial Dierential Equations. Two Types of Self-similarity. Strong Explosion 3. Self-similarity of Second Type and Condition on Index. Solution of the Rayleigh Problem in a Compressible Liquid. Tale 12. Calculation of the Sums, Landau Diamagnetism and the de Haas-van Alfven Eect 1. Watson-Sommerfeld Method 2. Euler-Maclaurin Method and Substitution a Sum by an Integral. 3. Poisson Method and Extracting an Oscillatory Part from the Sum. Tale 13. Soccer-ball and the Finite Group Representations 1. Geometry of a Socker-Ball 2. Two examples. 3. Donor in Ge 4. Icosahedral Group and its Character Table 5. Electron Levels of the Fullerene Molecule. 6. Hueckel Model 4 Tale 14 Painting of Polyhedrons or the Shubnikov Problem 1. Problem of stability of a painted gure. 2. The Indenbohm's Construction. 3. Superconductivity in Crystals and Zeros of the Gap Function. Tale 15, dedicated to M.D.Spector, on Dirichlet Principle and Geodesic Lines Tale 16. Variable Dimensionality and on Estimation of the Critical Depth of Potential Well Tale 17. Rainbows and Catastrophes 1. Geometric Optics. 2. Wave theory. Fringes. Airy Function. 3. General Catastrophes. Rainbow from Elliptic Drop. 4. Fringes from Elliptic Drop. Tale 18. Abrikosov's Lattice, Sunowers, Pineapples, Elliptic Functions and Modular forms Tale 19. Molecular Rotations and the Berry Phase Tale 20. Innities and Regularizations 1. Electron in magnetic eld and a random potential 2. Self-energy correction and its regularization 5 Tale 21 on Shape of Galaxies 1. Plasma Oscillations and Jeans Instability 2. Plasma Waves in Two Dimensions in Magnetic Field and Gallaxes Tale 22 on Dendrite Growth. 1. Ivantzov's regime and the patern selection problem. 2. Surface tension and the singular perturbation method. 3. Regime selection Tale 25 on Special Functions and Group Representations beginenumerate Hypergeometric function Group SL2(R), its structure and subgroups Lie algebra sl2(R). SO(n) and Gegenbauer Polynomials. 6 Tale 26. Can one heard the string shape. Inverse scattering problem. Tale 27 on Three Particles Collision and Tree Particles Bound State Tale 28 on Singular Integral Equations Tale 29 on Higher Order in Perturbation Theory 1. Ordinary Integral 2. Anharmonic Oscillator 3. QED Tale 30 on Boundary Layer and Submerged Jet. 1. Viscous ow and Reynolds number. Boundary layer, separation lines and turbulent tail. 2. Prandtl equations. 3. A wing in a ow. 4. Submerged jet. 7 Tale 31 on Stability of Propagating Fronts or ZeldovichBarenblatt Theorem Tale 32 on Hotzmark Distribution Tale 33 on Kaleidescope Tale 34 on Skirmions Tale 35 on Dice Tale 36 on Gaussian Integrals, Grassmannian Variables, Matrices and Determinants and on Super-symmetry. Tale 37. Proton Decay, Zero Modes and Attiyah - Singer Theorem Tale 38. Once more on Innities and regularisations. Quantum anomalies Tale 39 on Fluctuation of Distribution Function Tale 40 Lie Algebras and Dynamic Symmetry of Elementary Particles 1. Neutron 2. Deuton 3. Strange Particles 4. Search of Right Theory 8 Tale 41 by Shankar on Tiling Tale 42 on Frenet Formulae and Hyper-spiral Structure of DNA Tale 43 on Waterfalls and Shock Waves 1. Coastal Waves and Geometrical Optics 2. Waterfall. Waves of decompression. Riemann invariants 3. Waterfall. Shock waves. 9 The last fairy tale on Examples Answers to examples Reference Guide References Index NEW FAIRY TALES Tale 45 Spin and Oscillator Tale 46 Green Functions and Resistor's Networks Tale 47 Curvo-linear Coordinates Tale 48 2 in the exponent Tale 49 Knotes, Fermions and Ising model. Tale 50 Tale 51 Tale 52 10