A general account of modified Newtonian dynamics (MOND) theory is given. I start with the basic tenets of MOND, which posit departure from standard dynamics in the limit of low acceleration — below an acceleration constant a0 — where dynamics become scale invariant. I list some of the salient predictions of these tenets. The special role of a0 and its significance are then discussed. In particular, I stress its coincidence with cosmologically relevant accelerations, which may point to MOND having deep interplay with cosmology. The deep-MOND limit and the consequences of its scale invariance are considered in some detail. There are many ways to achieve scale invariance of the equations of motion — guaranteed if the total action has a well-defined scaling dimension. The mere realization that this is enough to ensure MOND phenomenology opens a wide scope for constructing MOND theories. General aspects of MOND theories are then described, after which I list briefly presently known theories, both nonrelativistic and relativistic. With few exceptions, the construction of known, full-fledged theories follows the same rough pattern: they modify the gravitational action; hinge on a0; introduce, already at the level of the action, an interpolating function between the low and high accelerations; and they obey MOND requirements in the two opposite limits. These theories have much heuristic value as proofs of various concepts (e.g., that covariant MOND theories can be written with correct gravitational lensing). But, probably, none points to the final MOND theory. At best, they are effective theories of limited applicability. I argue that we have so far explored only a small corner of the space of possible MOND theories. I then outline several other promising approaches to constructing MOND theories that strive to obtain MOND as an effective theory from deeper concepts, for example, by modifying inertia and (or) gravity as a result of interactions with some omnipresent agent. These have made encouraging progress in various degrees, but have not yet resulted in full-fledged theories that can be applied to all systems and situations. Some of the presently known theories do enjoy a natural appearance of a cosmological-constant-like contribution that, furthermore, exhibits the observed connection with a0. However, none were shown to address fully the mass discrepancies in cosmology and structure formation that are otherwise explained by cosmological dark matter. This may well be due to our present ignorance of the true connections between MOND and cosmology. We have no clues as to whether and how MOND aspects enter nongravitational phenomena, but I discuss briefly some possibilities.
Scale Invariance, Horizons, and Inflation
