1. Almost periodic functions -- 1. Almost periodic functions and Bohr compactilication -- 2. Besicovitch almost periodic functions and harmonic analysis -- 3. Structure of Bohr compactifications and spaces of almost periodic functions -- 4. Stepanov almost periodic functions -- 5. Weakly almost periodic functions -- 6. Spaces of smooth almost periodic functions on Rn -- Comments -- 2. Preliminaries -- 1. Some integral inequalities -- 2. Composition operators -- Comments -- 3. Solutions of evolution variational inequalities bounded and almost periodic in time -- 1. On variational inequalities -- 2. Bounded solutions -- 3. Regularity and almost periodicity of bounded solutions -- 4. The use of compactness -- 5. Almost periodicity in the sense of Besicovitch -- 6. Singular perturbation -- 7. Some examples and additional results -- Comments -- 4. Bounded and almost periodic solutions of certain evolution equations -- 1. Abstract evolution equations -- 2. Applications -- 3. Additional results -- Comments -- 5. Problems that are almost periodic in space variables -- 1. Nonlinear elliptic equations -- 2. Almost periodic first order systems -- 3. Symmetric hyperbolic systems with monotone nonlinearity -- 4. A nonlinear Schrödinger-type equation -- Comments -- Appendix 1. On certain linear evolution equations -- Appendix 2. On certain wave equations -- Appendix 3. Open questions -- References.