The DMAW 2010 LEGACY: the Presentation Review: Dark Matter in Galaxies" and its Explanatory Notes

The Seminar "Dark Matter in Galaxies" was delivered, within the Dark Matter Awareness Week (1-8 December 2010) at 140 institutes in 46 countries and it was followed by 4200 people. A documentation of this worldwide initiative is at http://www.youtube.com/watch?v=AOBit8a-1Fw. A reference presentation, prepared by a coordinated pool of leading scientists in the field, was available to speakers. In response to feedbacks and suggestions, we upgraded it to a "Presentation Review" of which we provide here the Explanatory Notes, the link to the .pptx file, and some image of the slides. This Presentation Review is an innovative scientific product to meet the request of information about the phenomenology of the DM mystery at galactic scale. This Review concerns the mass discrepancy phenomenon detected in galaxies, usually accounted by postulating the presence of a non luminous non baryonic component. In the theoretical framework of Newtonian Gravity we recall the properties of Dark Matter halos as emerging from the state-of-the-art of numerical simulations performed in the current $\Lambda CDM$ scenario. Then, the simple but much-telling phenomenology of the distribution of dark and luminous matter in Spirals, Ellipticals, and dwarf Spheroidals is reported. We show that a coherent observational framework emerges from reliable data of different large samples of objects and it is obtained by different methods of investigation. We then highlight the impressive evidence that the distribution of dark and luminous matter are closely correlated and that have universal features. Hints on the cosmological role of this phenomenological scenario are then given. Finally, we discuss the constraints on the elusive nature of the dark particle that the actual distribution of DM around galaxies pose on its direct and indirect searches.