Part I: Statics 1 Random walk models of polymer chains 1.1 Flexibility 1.2 The freely jointed chain 1.3 The freely rotating chain 1.4 Independent rotational potentials 1.5 The Gaussian chain 1.6 The Kratky–Porod model 1.7 Random walk in an external potential: The Edwards equation 2 Self-avoiding walks 2.1 Problem 2.2 Scale invariance 2.3 Flory theory 2.4 Computer simulations 2.5 The n→ 0 vector model 3 Self-consistent field theory 3.1 General approach 3.2 Flory screening of excluded–volume interactions 3.3 Free energy 3.4 Flory–Huggins theory 4 Blobology 4.1 Pincus blobs 4.2 Theta transition and thermal blobs 4.3 Overlap blobs 4.4 Generic phase diagram of a polymer solution Part II: Dynamics at and close to equilibrium 5 Equilibrium dynamics of dilute solutions 5.1 Rouse model 5.2 Zimm model 6 Linear viscoelasticity of dilute polymer solutions 6.1 The bead-spring chain 6.2 The diffusion equation 6.3 The stress tensor 6.4 Hookean dumbbells 6.5 Closure approximations for hydrodynamic interactions 6.6 Zimm model 6.7 Generalised Zimm model 6.8 Gaussian approximation 7 Equilibrium dynamics of semi-dilute solutions 7.1 Hydrodynamic screening and dynamic crossover scaling 7.2 Double crossover driven by temperature and concentration 7.3 Zero shear rate viscosity 8 Reptation model Tube concept, entanglement length, packing length, mean square displacement Part III: Dynamics far from equilibrium 9 Linear viscoelasticity of polymer melts 9.1 Nonlinear spring force laws 9.2 Non-bonded interactions 10 Dilute solutions 10.1 Nonequilibrium configurations and averages 10.2 FENE dumbbells 10.3 The Rouse and Zimm models 10.4 Fluctuating hydrodynamic interactions 11 Brownian dynamics simulations 11.1 Dilute solutions 11.2 Semi-dilute solutions Part IV: Background A Mathematical preliminaries A.1 The central limit theorem A.2 Brownian motion I: The Fokker–Plnack equation A.3 Brownian motion II: The Langevin equation A.4 Brownian motion III: Fluctuation–dissipation theorem B Some background from phase transitions B.1 Ising model B.2 Mean Field theory for the Ising model B.3 Critical exponents, scale invariance, scaling relations B.4 Upper critical dimension C Hydrodynamics C.1 Continuity and Euler equation C.2 Stress tensor and constitutive equations C.3 Viscous dissipation C.4 Stokes equation C.5 Oseen tensor C.6 Hydrodynamic interaction D Shear and shear free flows D.1 Kinematics D.2 Stress tensor D.3 Material functions