The Abbe invariant [1] defines the relationship between the input and output wavefront curvatures after refraction at a spherical surface. For the propagation of conical light pencils, it serves a role analogous to that of Snell’s law for individual light rays. The Lagrange invariant [2], conserved throughout an optical system, establishes a relationship between the pupil size, the field of view, and the refractive indices in the object and image spaces. Subsequently, the paraxial model is applied to derive expressions for the depth of focus and the positions of the principal planes in both a thick lens and a two-component optical system. Finally, ray transfer matrices are introduced as a universal method for analyzing paraxial optical systems and Gaussian light beams.