The monograph present ideas and methods, developed by the author, to solve the problem of existence of Bohr/Levitan almost periodic (respectively, almost recurrent in the sense of Bebutov, almost authomorphic, Poisson stable) solutions and global attractors of monotone nonautonomous differential/difference equations. Namely, the text provides answers to the following problems: 

1. Problem of existence of at least one Bohr/Levitan almost periodic solution for cooperative almost periodic differential/difference equations;  

2. Problem of existence of at least one Bohr/Levitan...