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1 Introduction    1.1 Studying molecular structure with 2D IR spectroscopy     1.2 Structural distributions and inhomogeneous broadening     1.3 Studying structural dynamics with 2D IR spectroscopy     1.4 Time domain 2D IR spectroscopy  2 Designing multiple pulse experiments     2.1 Eigenstates, coherences and the emitted field     2.2 Bloch vectors and molecular ensembles     2.3 Bloch vectors are a graphical representation of the density matrix     2.4 Multiple pathways visualized with Feynman diagrams     2.5 Rotating wave approximation     2.6 What is absorption?     2.7 Designing multi-pulse experiments     2.8 Selecting pathways by phase matching     2.9 Selecting pathways by phase cycling     2.10 Double sided Feynman diagrams: Rules  3 Mukamelian or Perturbative expansion of the density matrix     3.1 Density matrix     3.2 Time dependent perturbation theory  4 Basics of 2D IR spectroscopy     4.1 Linear spectroscopy     4.2 3rd-Order response functions     4.3 Time-domain 2D IR spectroscopy     4.4 Frequency-domain 2D IR spectroscopy     4.5 Transient pump-probe spectroscopy  5 Polarization control     5.1 Using polarization to manipulate the molecular response     5.2 Diagonal peak, no rotations     5.3 Cross peaks and orientations of coupled transition dipoles     5.4 Combining pulse polarizations: Eliminating diagonal peaks     5.5 Including (or excluding) rotational motions     5.6 Polarization conditions for higher-order pulse sequences  6 Molecular couplings     6.1 Vibrational excitons     6.2 Spectroscopy of a coupled dimer     6.3 Extended excitons in regular structures     6.4 Isotope labeling     6.5 Local mode transition dipoles     6.6 Calculation of coupling constants     6.7 Local versus normal modes     6.8 Fermi resonance  7 2D IR lineshapes    7.1 Microscopic theory of dephasing    7.2 Correlation functions    7.3 Homogeneous and inhomogeneous dynamics    7.4 Nonlinear response    7.5 Photon echo peak shift experiments 8 Dynamic cross peaks     8.1 Population transfer    8.2 Dynamic response functions    8.3 Chemical exchange 9 Experimental designs, data collection and processing    9.1 Frequency domain spectrometer designs    9.2 Experimental considerations for impulsive spectrometer designs    9.3 Capabilities made possible by phase control    9.4 Phase control devices    9.5 Data collection and data workup    9.6 Experimental issues common to all methods 10 Simple simulation strategies    10.1 2D lineshapes: Spectral di®usion of water    10.2 Molecular couplings by ab initio calculations     10.3 2D spectra using an exciton approach 11 Pulse sequence design: Some examples    11.1 2-Quantum pulse sequence    11.2 Rephased 2Q pulse sequence: 5th-Order spectroscopy    11.3 3D IR spectroscopy    11.4 Transient 2D IR spectroscopy    11.5 Enhancement of 2D IR spectra through coherent control    11.6 Mixed IR-Vis spectroscopies    11.7 Some of our dream experiments Appendix A  Fourier transformation  Appendix B  The ladder operator formalism Appendix C  Units and physical constants Appendix D  Legendre polynomials and spherical harmonics Appendix E  Recommended reading