Table of contents : Introduction to quantum many-sorted algebra Basics of deep learning Basic algebras underlying quantum and neural net Quantum Hilbert spaces and their creation Quantum and machine learning applications involving matrices Quantum annealing and adiabatic quantum computing Operators on Hilbert space Spaces and algebras for quantum operators Von Neumann algebra Fiber bundles Lie algebras and Lie groups Fundamental and universal covering groups Spectra for operators Canonical commutation relations Fock space Underlying theory for quantum computing Quantum computing applications Machine learning and data mining Reproducing kernel and other Hilbert spaces