This book presents a state space approach to the analysis of zeros of MIMO LTI discrete-time systems, using the Moore-Penrose pseudoinverse and singular value decomposition of the first nonzero Markov parameter of a system. The book begins with definition of invariant zeros and goes as far as a general characterization of output-zeroing inputs and the corresponding solutions, explicit formulas for maximal output-nulling invariant subspaces and for the zero dynamics.