Summary: An algebraic definition of the basic quantum process for the noncommutative stochastic calculus is given in terms of the Fock representation of a Lie *-algebra of matrices in a pseudo-Euclidean space. An operator definition of the quantum stochastic integral is given and its continuity is proved in a projective limit uniform operator topology. A new form of quantum stochastic equations, revealing the *- algebraic structure of quantum Itô's formula, is given.