Generally, spectroscopy refers to any experimental technique that uses electromagnetic radiation (such as visible light, ultraviolet light, x-rays, etc.) to give information about matter.

When electromagnetic radiation containing a range of frequencies encounters a material, the material absorbs the radiation, gains energy, and then emits radiation in response. However, the distribution of frequencies of radiation emitted by the material may be different from the frequencies that it absorbed. In this way, materials can be identified by the radiation that they emit.

Sometimes, however, a material will emit more than just radiation when it absorbs energy. In photoelectron spectroscopy, materials are exposed to high energy radiation, such as x-rays. As the materials absorb energy, some of the electrons in the atoms of the material gain enough energy that they can escape the material and fly away. By capturing these escaping electrons, you can learn information about atoms in the material, for example, how much energy is required to remove their electrons.

Photoelectron spectroscopy is also called photoemission spectroscopy. It is based on Albert Einstein's discovery (one of his many great discoveries) called "Photoelectric effect".

In late 19th century and early 20th century, there was a debate among scientists whether light should be viewed more like a "wave", or a "particle". Now we have understood that wave and particle are just two sides of the same coin, and we usually call this "particle-wave duality". But back then it was a big conceptual challenge in scientific community.

Einstein observed if light behaves like particles in some limit, it is capable of kicking out electrons from a solid, even though the electron was confined in the solid originally. This is called photoelectric effect (the quantum of light is called a photon), and has won Einstein a Nobel prize. After the photoelectric effect was confirmed experimentally, it has been used as a tool to inspect a material.

Photoelectron spectroscopy (usually) uses high energy photons to kick out electrons from a material, and uses the energy and angular change of the photon to study the internal structure and electronic properties of the material.

Photoelectron spectroscopy is also known as photo emission spectroscopy. It is a way to measure the electrons coming off solids, liquids, or gases.

Electrons are tiny particles that are a very important part of everything in the universe. Each electron has a negative charge. In photoelectron spectroscopy, electrons come off through what is known as the photoelectric effect, which is just a name for electrons coming off an object after light shines on the object - the "photo" part of the name refers to the light, which is made of little particles called photons. The technique of photoelectron spectroscopy is used to study characteristics of matter on extremely small, fundamental scales.

Photoelectron spectroscopy is also called photoemission spectroscopy. It is a surface analysis technique that measures the energy (and possibly momentum) of the emitted electrons by using the photoelectric effect. Since the binding energies of the emitted electrons depend on the chemical structure and molecular bonding, the measurement will provide information about the chemical environment of the substance under study.

The working principle and procedures are conceptually very easy. Photons (with proper energies depending on the material and technique) are prepared to hit the substance (can be solid, gas or liquid). The valence electrons can be scattered out by those photons. The conservation of energy and momentum during the scattering process (photoelectric effect) enables the determination of the energy and momentum of the emitted electrons possible, which reveals the key information about the chemical environment of the substance.

I haven't heard of it before, but doing a quick search I gather that it is a procedure by which sampled matter is bombarded with ionizing radiation to turn it into a plasma, and in the process ejecting electrons that have been knocked off of the atoms by the radiation. By analyzing the energy and number of these electrons, the analysis can determine what the sampled matter is made of. I am reminded of a similar method called gas chromatography and another called nuclear magnetic resonance, both of which use different techniques but have some similar functions and principles.

In photoelectron spectroscopy, you shine X-rays on a material, which excite electrons out of the material. These electrons come from different energy levels within the material, which tell you about what elements are inside, as well as the chemical identity of the elements (are they beside oxygen atoms, or is it a metal?).