In his recently published book 'A Brief History of Time', S. Hawking describes his remarkable insights into the problem of the origin of our universe. In this talk a more quantitative description of some of the important principles from this book is presented as a mathematical appendix to it. A brief review of the ideas of the Standard Big Bang Model of the Universe is given in terms of the evolution equation that follows from Einstein's theory. The meaning of the Cosmological Constant, its relation to Vacuum Energy, the model of the empty DeSitter Space and Gravity is derived. By analogy to Schrodinger mechanics one can give the general features of Quantum Cosmology', in which the origin of the universe can be viewed as a Quantum tunneling process in imaginary time from a Quantum Chaos state of no space, no time, no matter to an inflationary expanding DeSitter space which eventually transits into the Hot Big Bang Expansion that we see.