Manifestations of Dark Matter and Variations of the Fundamental Constants in Atoms and Astrophysical PhenomenaThis thesis explores the possibility of searching for new effects of dark matter that are linear in g, an approach that offers enormous advantages over conventional schemes, since the interaction constant g is very small, g<<1. Further, the thesis employs an investigation of linear effects to derive new limits on certain interactions of dark matter with ordinary matter that improve on previous limits by up to 15 orders of magnitude. The first ever