The book reviews the properties of surface plasmons that depict electromagnetic surface waves or surface plasma polaritons. Their propagation on smooth and corrugated surfaces (with rough or grating profiles) is considered. In the latter case, the corrugations can cause strong coupling of the surface plasmons with photons leading to resonances with a strong enhancement of the electromagnetic field in the surface. Coupling and field enhancement are the most prominent phenomena on corrugated surfaces and lead to numerous important applications. Attention has been focused on the explanation of the physics. To keep the text readable, sophisticated calculations have been avoided, and instead various applications dealing with enhanced light emission, nonlinear optics, SERS, and other cases of interest are discussed.