Mathematical quantum physics : a foundational introduction This book provides the rigorous mathematical foundations of Quantum Physics from the operational meaning of the measuring process to the most recent theories for the quantum scale of space time geometry. Topics like relativistic invariance quantum systems with finite and infinitely many degrees of freedom second quantisation scattering theory are all presented through the formalism of Operator Algebras for a precise mathematical justification. The book is targeted to graduate students and researchers in the area of theoretical mathematical physics who want to learn about the mathematical foundations of quantum physics as well as the mathematics students and researchers in the area of operator algebras functional analysis who want to dive into some of the applications of the theory to physics. .