The stress driven cortisol dynamics of the Hippocampal-Hypothalamic-(Anterior) Pituitary-Adrenal (HHPA) axis with its negative feedback loops from the adrenals to pituitary and hypothalamus, in particular relation with hippocampus, have been the focus of the last few years boom of papers using various distinctive mathematical models, simulations, stability analyses and optimal control of these models. These many quantitative approaches led to discovering unknown connections between cortisol feedback loop dysfunctions and stress disorders (post-traumatic stress disorder (PTSD), depression, chronic fatigue syndrome (CFS)), adrenal suppression and atrophy, Alzheimer (AD) and hypocampal cognitive dysfunctions (memory loss) leading to new drug treatment strategies.We assemble here together and unify these results, including our own early work, in order to create an integrative mathematical system theory framework for HHPA & HPA and stress driven cortisol dynamics in which various clinical disorders appear as various quantifiable negative feedback loop dysfunctions and drug therapies correcting these disorders appear as feedback model based treatments: a neuroendocrine system theory for cortisol "feedback pathology" and its existing and future possible "feedback therapies".