A self-contained introduction to the main aspects of high-power laser-matter interaction in the intensity range 10^10-10^22 W/cm^2 from plasma formation to highly relativistic interactions of the laser field with matter is presented. It is intended as a guide for scientists and students who have just discovered the field as a new and attractive area of research, and for scientists who have worked in another field and want to join now the subject of laser plasmas. In the first chapter the plasma dynamics is described phenomenologically by a two fluid model and similarity relations from dimensional analysis. Chapter 2 is devoted to plasma optics and collisional absorption in the dielectric and ballistic model. Linear resonance absorption at the plasma frequency and its mild nonlinearities as well as the self-quenching of high amplitude electron plasma waves by wave breaking are discussed in Chapter 3. With increasing laser intensity the plasma dynamics is dominated by radiation pressure, at resonance producing all kinds of parametric instabilities and out of resonance leading to density steps, self-focusing and filamentation, described in Chapters 4 and 5.A self-contained treatment of field ionization of atoms and related phenomena are found in Chapter 6. The extension of laser interaction to the relativistic electron acceleration as well as the physics of collisionless absorption are the subject of Chapter 7. Throughout the book the main emphasis is on the various basic phenomena and on their underlying physics.