The monograph deals with the properties of layered finite groups, i.e. groups with finite sets of elements of each order. Layer-wise finite groups are characterized in other group classes, namely it is shown how layer-wise finite groups are embedded in the class of locally normal groups - this is a classical characterization; then layer-wise finite groups are embedded in the classes of binary solvable and periodic groups - these are already the results of recent years. The book is of interest to academic, undergraduate and graduate students specializing in algebra.