This article provides an introduction to the essential concepts and terminology in strong gravitational lensing. It emphasizes physical insight and explains the key construct of the Fermat potential or arrival-time surface, from which the standard lens equation and related notions such as image parities, magnification, critical curves, caustics, and degeneracies follow. The advantages and limitations of simplifying assumptions like geometrical optics, small angles, weak fields, and thin lenses are discussed. The article also explores how to go beyond these assumptions and discusses less well-known ideas, such as wavefront arguments showing that much of the theory applies to strong gravitational fields and saddle-point contours explaining how even complex image configurations consist of two ingredients. It also addresses orders of magnitude and the question of why strong lensing is most common for objects at cosmological distances. The challenges of lens modeling and diverse strategies to overcome them are discussed in general terms without many technical details. The article covers the general picture of gravitational lensing, including light deflection, wavefronts, and Fermat's principle, as well as the cosmological context, distances in cosmology, the lens and source planes, and the standard formalism of gravitational lensing. It explains the Einstein radius, the three kinds of images, magnification, and critical curves and caustics. The article concludes with a discussion of the implications of these concepts for understanding strong gravitational lensing.This article provides an introduction to the essential concepts and terminology in strong gravitational lensing. It emphasizes physical insight and explains the key construct of the Fermat potential or arrival-time surface, from which the standard lens equation and related notions such as image parities, magnification, critical curves, caustics, and degeneracies follow. The advantages and limitations of simplifying assumptions like geometrical optics, small angles, weak fields, and thin lenses are discussed. The article also explores how to go beyond these assumptions and discusses less well-known ideas, such as wavefront arguments showing that much of the theory applies to strong gravitational fields and saddle-point contours explaining how even complex image configurations consist of two ingredients. It also addresses orders of magnitude and the question of why strong lensing is most common for objects at cosmological distances. The challenges of lens modeling and diverse strategies to overcome them are discussed in general terms without many technical details. The article covers the general picture of gravitational lensing, including light deflection, wavefronts, and Fermat's principle, as well as the cosmological context, distances in cosmology, the lens and source planes, and the standard formalism of gravitational lensing. It explains the Einstein radius, the three kinds of images, magnification, and critical curves and caustics. The article concludes with a discussion of the implications of these concepts for understanding strong gravitational lensing.