Quantum Limit Spectroscopy This book covers the main ideas methods and recent developments of quantum limit optical spectroscopy and applications to quantum information resolution spectroscopy measurements beyond quantum limits measurement of decoherence and entanglement. Quantum limit spectroscopy lies at the frontier of current experimental and theoretical techniques and is one of the areas of atomic spectroscopy where the quantization of the field is essential to predict and interpret the existing experimental results. Currently there is an increasing interest in quantum and precision spectroscopy both theoretically and experimentally due to significant progress in trapping and cooling of single atoms and ions. This progress allows one to explore in the most intimate detail the ways in which light interacts with atoms and to measure spectral properties and quantum effects with high precision. Moreover it allows one to perform subtle tests of quantum mechanics on the single atom and single photon scale which were hardly even imaginable as ``thought experiments a few years ago 1. Quantum Fluctuations and Their Measurements 2. Spectra of Radiating Systems 3. Spectroscopy with Single Atoms in Atomic Beams 4. Collective Multiatom Spectroscopy 5. Time Dependent Fluorescence Spectroscopy 6. Quantum Spectroscopy with Squeezed Light 7. Experiments with Squeezed Light Excitation of Atoms 8. Engineering Collective and Squeezed Field Interactions 9. Beating Quantum Limits in Optical Spectroscopy 10. Dipole Squeezing and Spin Squeezed States