In recent years, the classical theory of shastic integration and shastic differential equations has been extended to a non-commutative set-up to develop models for quantum noises. The author, a specialist of classical shastic calculus and martingale theory, tries to provide an introduction to this rapidly expanding field in a way which should be accessible to probabilists familiar with the Ito integral. It can also, on the other hand, provide a means of access to the methods of shastic calculus for physicists familiar with Fock space analysis. For this second edition, the author has added about 30 pages of new material, mostly on quantum shastic integrals.