  For solid-state materials, the electronic structure, E(k), is critical in
determining a crystal's physical properties. By experimentally detecting the
electronic structure, the fundamental physics can be revealed. Angle-resolved
photoemission spectroscopy (ARPES) is a powerful technique for directly
observing the electronic structure with energy- and momentum-resolved
information. Over the past decades, major improvements in the energy and
momentum resolution, alongside the extension of ARPES observables to spin
(SpinARPES), micrometer or nanometer lateral dimensions (MicroARPES/NanoARPES),
and femtosecond timescales (TrARPES), have led to major scientific advances.
These advantages have been achieved across a wide range of quantum materials,
such as high-temperature superconductors, topological materials,
two-dimensional materials and heterostructures. This primer introduces key
aspects of ARPES principles, instrumentation, data analysis, and representative
scientific cases to demonstrate the power of the method. Perspectives and
challenges on future developments are also discussed.
