This book develops a new physical/mathematical model for the functioning of the human brain, based, not on the modern Newton-Einstein view of physical reality, but on 'information reality'. The work is devoted to the physical-mathematical modeling of (conscious) cognitive phenomena. The most important distinguishing feature of the theory presented here is a new model of mental space, the so-called p-adic hierarchic tree space, and the development of mental analogs of classical and quantum mechanics. Mental processes and more general information processes are handled as a kind of new physical processes. In particular, the procedure of information quantization and an information analog of Bohmian mechanics are developed. Here, mind is a singularity in the mental pilot wave. Applications to neurophysiology, localization of mental function and brain ablations, and psychology (in particular, Freud's psychoanalysis) are considered.