Includes bibliographical references and index.

Fluctuations, renormalization and universality -- Fluctuations and universality in condensed matter physics -- The universal Prandtl number in two-dimensional hydrodynamics -- The universal Poisson ratio in fluctuating polymerized membranes -- Defect-mediated phase transitions and hydrodynamic theories -- The contents of this book -- Renormalization -- The self-dual point of Ising spins in two dimensions -- Defect-mediated phase transitions -- The XY model and superfluidity in two dimensions -- Dynamic scaling and third sound in helium films -- Statistical mechanics of two-dimensional melting -- Melting dynamics -- Anisotropic melting -- Line singularities in three dimensions -- Order, frustration and two-dimensional glass -- Order and frustration in quenched binary arrays -- Order and frustration in spaces of incommensurate curvature -- The structure and statistical mechanics of three-dimensional glass -- A physical picture -- The model free energy -- The statistical mechanics of crumpled membranes -- Flat surfaces -- Crumpled membranes -- Normal-normal correlations in liquid membranes -- Tethered surfaces with bending energy -- Defects and hexatic order in membranes -- Defects in superfluids, superconductors and membranes -- Two-dimensional superfluids and superconductors -- Defects in membranes and monolayers -- Superfluid density and momentum correlations -- Vortex-line fluctuations in superconductors from elementary quantum mechanics -- Correlated pinning and quantum bound states -- Flux melting and the quantum harmonic oscillator.

Thermally excited defects such as vortices, disclinations, dislocations, vacancies and interstitials play a key role in the physics of crystals, superfluids, superconductors, liquid crystals and polymer arrays. Geometrical aspects of statistical mechanics become particularly important when thermal fluctuations entangle or crumple extended line-like or surface-like objects in three dimensions. In the case of entangled vortices above the first-order flux lattice melting transition in high temperature superconductors, the lines themselves are defects. A variety of low temperature theories combined with renormalization group ideas are used to describe the delicate interplay between defects, statistical mechanics and geometry characteristic of these problems in condensed matter physics. David Nelson provides a coherent and pedagogic graduate level introduction to the field of defects and geometry.