The publication is devoted to the presentation of the basics of methods for calculating the propagation of one-dimensional and electromagnetic waves through multilayer structures. The impedance, exclusion and re-reflection methods determine the parameters of the propagating waves, as well as the reflection and transmission coefficients depending on the energy. The focus is on impedance methods, as well as an elimination method that is quite universal in nature and allows simple machine algorithmization for structures with an arbitrary number of layers. A diagram of the re-reflection method is presented, which is of significant value for a number of specific cases. Some problems of an applied nature have been solved. There are many examples and guidelines for independent work of students.