Topics: Quantum Description of Decaying Meta-Stable States with Applications in Physics, Chemistry, and Engineering: a Survey of Resonanace Phenomena in Physics, Chemistry and Engineering. Feshback Type Resonances and Shape Type Resonance, Methods for Observing Rersonance in Hamiltonian Quantum Mechanics, Non-Hermitian Quantum Mechanics, Analytic Continuation of the Hamiltonian and Compex Scaling Methods, the Advantages of Studying Resonances by Non-Hermitian Quantum Mechanics. Computational Methods and Algorithms for Evaluating Resonance Energies and Lifetime. Applications of Nonhamiltonian Quantum Mechanics to the Study of Resonances in Atomic, Molecular and Laser Driven Systems. Applications to the Transmission Light through Otical Waveguides. Applications of the Theory to Different Fields of Natural Sciences.