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Contents: Nonlinear Problems in 1+ 1 and Their LinearizationClassical Field Theory ModelsHamiltonian Formulation, Action-Angle Variables, Solitons, Classical Lattice Models and Lattice Approximants of Classical FieldsQuantization on a Lattice: Relationship Classical-QuantumQuantization on a Lattice: Simple Bose ModelsSpin 1/2 Lattice Systems Related to Nonlinear Bose Problems: Lattice FermionsQuantization in Continuum: Joint Bose-Fermi Spectral Problems in 1+ 1Quantum Meaning of Classical Field Theory for Fermi SystemsOn Infinite Constituent “Elementary” Systems: Canonical (Constituent) Quantization of Soliton FieldsTowards 1+ 3: Problems and Prospects Readership: Mathematical physicists and physicists. Keywords: Nonlinear Fields; Integrability; Solvable Models; Solitons; Continuum and Lattice Models; Quantization; Fermi Fields And Their Classical Counterparts; Relationship Classical-Quantum; Boson-Fermion Reciprocity (Bosonization)