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1. Introduction 982. Historical background of two-photon effects 992.1 2PE 1002.2 Harmonic generation 1002.3 Fluorescence correlation spectroscopy 1003. Basic principles of two-photon excitation of fluorescent molecules and implications for microscopy and spectroscopy 1013.1 General considerations 1013.2 Fluorescence intensity under the 2PE condition 1033.3 Optical consequences of 2PE 1043.4 Saturation effects in 2PE 1083.5 Fluorescence correlation spectroscopy 1093.5.1 Autocorrelation analysis 1103.5.2 Photon-counting histogram analysis 1124. Two-photon-excited probes 1155. Design considerations for a 2PE fluorescence microscope 1195.1 General aspects 1195.2 Descanned and non-descanned 2PE imaging 1215.3 Lens objectives and pulse broadening 1225.4 Laser sources 1255.5 Example of a practical realization 1276. Applications 1346.1 Biological applications of 2PE 1346.1.1 Brain …