The basic ideas of the superstring approach in the physics of elementary particles are presented at a rather simple theoretical level. The theory of interacting superstrings with dimensions of the order of the Planck dimension is presently regarded as a fundamentally new and extremely promising approach to a unification of all the fundamental interactions (strong, electromagnetic, weak, and gravitational) in a common theoretical framework. Although this field is still in a stage of rapid development, several results of definite interest have been obtained. The classical dynamics and the quantum dynamics of boson and spin strings are described. Such strings arise primarily in hadron physics. How a critical dimensionality of space-time and tachyon states arise upon the quantization of string models is demonstrated. A superstring is a supersymmetric generalization of very simple models of a relativistic string. The total action of a superstring is examined. The field theory of superstrings is discussed, as are various methods for introducing internal symmetries in string theories. The low-energy (field) limit in superstring theory is studied. The cancellation of anomalies and the problem of divergences are discussed. Compactification in superstring theories is discussed, as is a phenomenology which arises here for the modern physics of elementary particles. Some cosmological consequences of the superstring approach are outlined.