Short answers, pulled from the story.
Absorption spectroscopy measures the electromagnetic radiation absorbed by a sample as a function of frequency or wavelength. A beam of radiation is directed at the sample, and the intensity of radiation that passes through is detected. The difference between the incident and transmitted radiation reveals the sample's absorption spectrum.
Absorption spectroscopy can identify specific substances in a mixture, quantify the amount of a substance present, determine molecular bond lengths and angles, detect atmospheric pollutants, and analyze the composition of extrasolar planet atmospheres. The Beer-Lambert law connects measured absorption to the concentration of the absorbing substance.
Absorption spectroscopy spans the full electromagnetic spectrum: X-rays, ultraviolet-visible light, infrared, microwaves, and radio waves. Each spectral region corresponds to a different type of quantum mechanical transition, including electronic, vibrational, rotational, and inner-shell electron excitations.
Astronomical spectroscopy uses absorption spectra to study objects too distant to reach physically. It has been used to determine that some interstellar clouds contain molecules and to analyze the atmospheric composition, temperature, pressure, and scale height of extrasolar planets detected by transit photometry.
The Lamb shift is a small energy difference measured in the hydrogen atomic absorption spectrum that was not predicted to exist when it was first observed. Its discovery guided the development of quantum electrodynamics, and measurements of the Lamb shift are now used to determine the fine-structure constant.
Differential optical absorption spectroscopy is used for remote sensing. It focuses on narrow differential absorption features while omitting broad-band effects such as aerosol extinction and Rayleigh scattering. The method is applied to ground-based, airborne, and satellite-based measurements and can retrieve trace gas profiles in the troposphere and stratosphere.