1. Introduction No less than 99.9% of the matter in the visible Universe is in the plasma state. The plasma is a gas in which a certain portion of the particles are ionized, and is considered to be the "fourth" state of the matter. The Universe is filled with plasma particles ejected from the upper atmosphere of stars. The stream of plasma is called the stellar wind, which also carries the intrinsic magnetic field of the stars. Our solar system is filled with solar-wind-plasma particles. Neutral gases in the upper atmosphere of the Earth are also ionized by a photoelectric effect due to absorption of energy from sunlight. The number density of plasma far above the Earth's ionosphere is very low (∼100cm −3 or much less). A typical mean-free path of solar-wind plasma is about 1AU 1 (Astronomical Unit: the distance from the Sun to the Earth). Thus plasma in Geospace can be regarded as collisionless. Motion of plasma is affected by electromagnetic fields. The change in the motion of plasma results in an electric current, and the surrounding electromagnetic fields are then modified by the current. The plasma behaves as a dielectric media. Thus the linear dispersion relation of electromagnetic waves in plasma is strongly modified from that in vacuum, which is simply˜ω simply˜ simply˜ω = kc where˜ωwhere˜ where˜ω, k,a n dc represent angular frequency, wavenumber, and the speed of light, respectively. This chapter gives an introduction to electromagnetic waves in collisionless plasma 2 , because it is important to study electromagnetic waves in plasma for understanding of electromagnetic environment around the Earth. Section 2 gives basic equations for electromagnetic waves in collisionless plasma. Then, the linear dispersion relation of plasma waves is derived. It should be noted that there are many good textbooks for linear dispersion relation of plasma waves. However, detailed derivation of the linear dispersion relation is presented only in a few textbooks (e.g., Stix, 1992; Swanson, 2003; 2008). Thus Section 2 aims to revisit the derivation of the linear dispersion relation. Section 3 discusses excitation of plasma waves, by providing examples on the excitation of plasma waves based on the linear dispersion analysis. Section 4 gives summary of this chapter. It is noted that the linear dispersion relation can be applied for small-amplitude plasma waves only. Large-amplitude plasma waves sometimes result in nonlinear processes. Nonlinear processes are so complex that it is difficult to provide their analytical expressions, and computer simulations play important roles in studies of nonlinear processes, which should be left as a future study. The book collects original and innovative research studies of the experienced and actively working scientists in the field of wave propagation which produced new methods in this area of research and obtained new and important results. Every chapter of this book is the result of the authors achieved in the particular field of research. The themes of the studies vary from investigat...

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