1.introduction 2.the independent-electron approximation 2.1 starting hamiltonian 2.2 basis functions and basis sets 2.3 self-consistent field approximation 2.4 simplified scf calculational schemes 2.4.1 semi-empirical scf methods 2.4.2 pseudopotentials 2.5 koopmans' theorem 2.6 homogeneous electron gas 2.7 local exchange potential - the xa method 2.8 shortcomings of the independent-electron approximation 2.9 unrestricted scf approximation 3.density functional theory 3.1 thomas-fermi method 3.2 hohenberg-kohn-sham theory 3.3 local-density approximation 3.4 results for atoms, molecules, and solids 3.5 extensions and limitations 4.quantum-chemical approach to electron correlations 4.1 configuration interactions 4.1.1 local and localized orbitals 4.1.2 selection of double substitutions 4.1.3 multireference ci 4.2 many-body perturbation theory 5.cumulants, partitioning, and projections 5.1 cumulant representation 5.1.1 ground-state energy 5.1.2 perturbation expansion 5.2 projection and partitioning techniques 5.2.1 coupled-electron-pair approximations 5.2.2 projections based on local operators 5.2.3 method of increments 5.3 coupled-cluster method 5.4 comparison with various trial wavefunctions 5.5 simplified correlation calculations 6.excited states 6.1 ci calculations and basis set requirements 6.2 excitation energies in terms of cumulants 6.3 green's function method 6.3.1 perturbation expansions 6.3.2 the projection method 6.4 local operators 7.finite-temperature techniques 7.1 approximations for thermodynamic quantities 7.1.1 temperature green's function 7.1.2 the projection method for t 4:0 7.2 functional-integral method 7.2.1 static approximation 7.3 monte carlo methods 7.3.1 sampling techniques 7.3.2 ground-state energy 8.correlations in atoms and molecules 8.1 atoms 8.2 hydrocarbon molecules 8.2.1 analytic expressions for correlation-energycontributions 8.2.2 simplified correlation calculations 8.3 molecules consisting of first-row atoms 8.4 strength of correlations in different bonds 8.5 polymers 8.5.1 polyethylene 8.5.2 polyacetylene 8.6 photoionization spectra 9.semiconductors and insulators 9.1 ground-state correlations 9.1.1 semi-empirical correlation calculations 9.1.2 ab initio calculations 9.2 excited states 9.2.1 role of nonlocal exchange 9.2.2 the energy gap problem 9.2.3 hedin's gw approximation 10.homogeneous metallic systems 10.1 fermi-liquid approach 10.2 charge screening and the random-phase approximation 10.3 spin fluctuations 11.transition metals 11.1 correlated ground state 11.2 excited states 11.3 finite temperatures 11.3.1 single-site approximation 11.3.2 two-sites approximation 11.3.3 beyond the static approximation 12.strongly correlated electrons 12.1 molecules 12.2 anderson hamiltonian 12.2.1 calculation of the ground-state energy 12.2.2 excited states 12.2.3 noncrossing approximation 12.3 effective exchange hamiltonian 12.3.1 schrieffer-wolff transformation 12.3.2 kondo divergency 12.3.3 fermi-liquid description 12.4 magnetic impurity in a lattice of strongly correlatedelectrons 12.5 hubbard hamiltonian 12.5.1 ground-state: gutzwiller's wavefunction and spin-densitywave state 12.5.2 excitation spectrum 12.5.3 the limits of one dimension and infinite dimensions 12.6 the t - j model 12.7 slave bosons in the mean-field approximation 12.8 kanamori's t-matrix approach 13.heavy-fermion systems 13.1 the fermi surface and quasiparticle excitations 13.1.1 large versus small fermi surface 13.2 model hamiltonian and slave bosons 13.3 application of the noncrossing approximation 13.4 variational wavefunctions 13.5 quasiparticle interactions 13.6 quasiparticle-phonon interactions based on strongcorrelations 14.superconductivity and the high-te materials 14.1 the superconducting state 14.1.1 pair states 14.1.2 bcs ground state 14.1.3 pair breaking 14.2 electronic properties of the high-tc materials 14.2.1 electronic excitations in the cu-o planes 14.2.2 calculation of the spectral weight by projectiontechniques 14.2.3 size of the fermi surface 14.3 other properties of the cuprates 14.3.1 loss of antiferromagnetic order 14.3.2 optical conductivity 14.3.3 magnetic response 14.4 heavy fermions in nd2_xcexcuo4 appendix a.relation between exc[p] and the pair distribution function b.derivation of several relations involving cumulants c.projection method of mori and zwanzig d.cross:over from weak to strong correlations e.derivation of a general form for ω） f.hund's rule correlations g.cumulant representation of expectation values and correlationfunctions h.diagrammatic representation of certain expectation values i.derivation of the quasiparticle equation j.coherent-potential approximation k.derivation of the nca equations l.ground-state energy of a heisenberg antiferromagnet on a squarelattice m.the lanczos method references subject index
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