This book presents an advanced-level reorganization of the probability theory of quantum theory based on multiple quantum events in terms of consecutive and conditional probability. This leads to the recognition that the fundamental quantum time evolution equation, instead of the Schrödinger's equation, is the Generalized Born's Rule, which has a valid (though secondary) role in one model of the axioms of quantum theory usually called the Schrödinger picture. So, this approach is fully consistent with textbook quantum theory. This new approach clarifies the 'paradoxes' in quantum theory of entanglement and collapse. There are few references to classical physics, given that this is a new stand-alone axiomatic presentation of quantum theory. Notice that this is not an 'interpretation' of quantum theory as that word is usually understood. The intended audience consists of scientists, philosophers and students who preferably have some previous knowledge of quantum theory.