A mathematical journey to quantum mechanics This book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined. The material covers topics such as analytic mechanics in Newtonian Lagrangian and Hamiltonian formulations theory of light as formulated in special relativity and then why quantum mechanics is necessary to explain experiments like the double split atomic spectra and photoelectric effect. The Schrödinger equation and its solutions are developed in detail. It is pointed out that starting from the concept of the harmonic oscillator it is possible to develop advanced quantum mechanics. Furthermore the mathematics behind the Heisenberg uncertainty principle is constructed towards advanced quantum mechanical principles. Relativistic quantum mechanics is finally considered. The book is devoted to undergraduate students from University courses of Physics Mathematics Chemistry and Engineering. It consists of 50 self contained lectures and any statement and theorem are demonstrated in detail. It is the companion book of A Mathematical Journey to Relativity by the same Authors published by Springer in 2020.