This article provides an introduction to the essential concepts and terminology of strong gravitational lensing, emphasizing physical insight. It begins by explaining the basic phenomenon of gravitational lensing, where quasars and high-redshift galaxies appear as multiple images due to the gravitational lensing effect of foreground galaxies and clusters. The key construct is the Fermat potential or arrival-time surface, from which the standard lens equation, image parities, magnification, critical curves, caustics, and degeneracies follow. The article discusses the advantages and limitations of simplifying assumptions such as geometrical optics, small angles, weak fields, and thin lenses, and explains how to extend the theory beyond these assumptions. It also explores less well-known ideas, such as arguments using wavefronts and saddle-point contours, and discusses 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 also covered. The article concludes with a discussion of the cosmological context, including the threshold acceleration for strong lensing and the different ways of expressing distances in cosmology.This article provides an introduction to the essential concepts and terminology of strong gravitational lensing, emphasizing physical insight. It begins by explaining the basic phenomenon of gravitational lensing, where quasars and high-redshift galaxies appear as multiple images due to the gravitational lensing effect of foreground galaxies and clusters. The key construct is the Fermat potential or arrival-time surface, from which the standard lens equation, image parities, magnification, critical curves, caustics, and degeneracies follow. The article discusses the advantages and limitations of simplifying assumptions such as geometrical optics, small angles, weak fields, and thin lenses, and explains how to extend the theory beyond these assumptions. It also explores less well-known ideas, such as arguments using wavefronts and saddle-point contours, and discusses 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 also covered. The article concludes with a discussion of the cosmological context, including the threshold acceleration for strong lensing and the different ways of expressing distances in cosmology.