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This article presents an extensive review of the status of the search of the dark matter. The first eight sections are devoted to topics in dark matter and its experimental searches, and the rest to selected topics in astrophysics and cosmology, which are intended to supply some of the needed background for students in particle physics. Sections 9 and 13 are introductory cosmology. The three astrophysical topics, Big Bang nucleosynthesis Section 10, Boltzmann transport equation and freeze out of massive particles Section 11, and CMB anisotropy Section 12 can all be studied in analytical approaches when reasonable approximations are made. Their original analytically forms, to which this article follows very closely, were given by particle physicists. Dark matter is an evolving subject requiring timely update to stay current. Hence a review of such a subject matter would undoubtedly have something wanting when it appears in print. It is hoped that this review can form a humble basis for those graduate students who would like to pursue the subject of dark matter. The reader can use the extensive table of contents to see in some details the materials covered in the article.

Atomic nuclei comprise a principal level of material structure. Nuclear physics, in itself an substantial area of study, serves as a link between atomic physics and particle physics. The main research areas of nuclear physics involve strong interaction, weak interaction, and electromagnetic interaction.

In the standard model of particle physics, photons are massless particles with a particular dispersion relation. Tests of this claim at different scales are both interesting and important. Experiments in territory labs and several exterritorial tests have put some upper limits on photon mass, e.g., torsion balance experiment in the lab shows that photon mass should be smaller than 1.2 x 10-51g. In this work, this claim is tested at a cosmological scale by looking at strong gravitational lensing data available and an upper limit of 8.71 x 10-39g on photon mass is given. Observations of energy-dependent gravitational lensing with not yet available higher accuracy astrometry instruments may constrain photon mass better.

Higgs type excitations are the excitations which give mass to particles. The Higgs type excitations has a critical role both in particle physics and condensed matter physics. In particle physics, the suspected Higgs boson has been found by the Large Hadron Collider （LHC） in 2012. In condensed matter physics, the Higgs type excitations relate to order phase of the system. In this review, we present an overview of recent studies on the Higgs type excitations both in non-interacting and interacting cold atom systems. First, in non-interacting cold atom system, by synthesizing artificial non-Abelian gauge potential, we demonstrate that when a non- Abelian gauge potential is reduced to Abeliau potential, the Abelian part constructs spin-orbit coupling, and the non-Abelian part emerges Higgs excitations. Secondly, the Higgs excitations which are the reputed Higgs amplitude mode in interacting cold atom system are discussed. We review the theoretical model and the experimental detection of Higgs amplitude mode in two dimensional superfluid. The observation of both Higgs type excitations in real experiments are also discussed.