We show that quadratic spaces are a fundamental clue to understand the structure of theoretical physics. Classical Physics is embedded within a 5-D flat quadratic space, 3 Space-, one Time- and one Action- like basis manifolds (Lorentz signature 1,4) faithfully providing a Relativistic Theory (START) describing Newtonian, Maxwell, geometrical optics and General Relativity as particular linear and quadratic forms of this (flat) START space. The 5-D space has a quadratic form which maps into the real quadratic form of a (hyperbolic-complex) 4-D space-time dS² = dS • dS† . Otherwise the understanding of a many electron quantum mechanical (QM) system, with all its QM intricacies, is presented considering the QM “density” as a quadratic form and the QM “wave function” as its corresponding linear form.