Postmodern logarithmo-technia

In order to solve ordinary differential equations, we use an equation with the so-called logarithmic derivative. Similar equations with a linear operator permit us to define logarithmic and antilogarithmic mappings and obtain some results unknown before for the classical derivation operator. This method and its applications are exposed in detail in the authorʹs book [1] and may be treated as an introduction into the 21st century logarithmo-technia (according to the original meaning of this word). In the first section, there are given basic notions and facts of algebraic analysis (without proofs). The second section consists of the most important definitions and theorems (without proofs) concerning logarithms and antilogarithms. The third section is concerned with properties of multiplicative true shifts. In the last section is given a generalization of the binomial theorem for harmonic logarithms.