Chapter I (the Introduction) formulates the problem of the spiral structure. A survey of recent observational data on the structure of spiral galaxies is given in Chap. II. Data are submitted on the physical composition of the spiral arms, the distribution of the stellar and gaseous constituents of the galaxies, and the physical state of the interstellar medium. Chapter III deals with the wave theory of spiral structure. In the contemporary conception, the spiral arms are waves propagating in the galaxy at frequencies determined by some exciting mechanism (a generator), with their wave number determined by the dispersion properties of the galaxy. In this approach, the speed of rotation of the spiral pattern, which equals the frequency divided by the number of arms, does not depend on the distance to the center of the galaxy; this eliminates the problem of the twisting of the spiral arms by differential rotation. The conclusions of the wave theory are discussed, and a dispersion equation is given for the spiral structure of a galaxy. The problem of generation and maintenance of the sprial pattern is discussed. Numerical galaxy-modeling experiments are examined in Chap. IV. These experiments point to the formation of spiral structures of wave nature in disciform systems of gravitating particles. Critical remarks concerning the numerical experiments are offered. The Conclusion (Chap. V) discusses arguments for and against the wave theory. It is noted that this theory explains many of the observed facts and that many of its predictions have also been confirmed by observations.