Single lenses with real thickness refract the different wavelengths of light at slightly different angles. For anywhere other than the exact optical center of the lens, this causes a prismatic effect that gets more noticeable as one moves further from the optical center of the lens. This is what we refer to as chromatic aberration. It isn't the only optical aberration we encounter when using a single lens element, but it is probably the most noticeable one.

The earliest spyglasses (telescopes) suffered greatly from CA and the other optical aberrations. The field of optics developed to deal with these imperfections as they applied to telescopes well before the beginning of photography in the mid-19th century as a means of preserving a scene projected by a lens using light sensitive chemicals.

In the 1600's, Snellius (the origin of 'Snell's Law') and Descartes (the creator or Cartesian geometry) codified the earliest laws of refraction and reflection. By 1690 Christiaan Huygens had written his 'Traité de la Lumière' or 'Treatise on Light' that built on Descartes' work and presented the wave theory of light, first presented to the Paris Academy of Sciences in 1678, based on mathematics. Isaac Newton published 'Hypothesis of Light' in 1675 and 'Optiks' in 1705 in which he presented a competing theory of light as corpuscles, or particles. For the next hundred years or so, Newton's theory of light was accepted and Huygens' wave theory was rejected. It was not until Augustin-Jean Fresnel adopted Huygens' principle in 1821 and showed that it could explain the rectilinear propagation and diffraction effects of light that Huygens' wave theory was generally accepted. This principle is now known as the Huygens–Fresnel principle.

Newton also demonstrated that a prism decomposes white light into a spectrum of its component colors, and that a lens and second prism can be used to recompose the multicolored spectrum back into white light that had the same properties as the light before it struck the first prism. Although the particulars of Newton's corpuscular theory has been shown to be mostly incorrect, his breakthroughs with regard to color and refraction, along with similar work by Huygens, are what led to the development of compound lenses to correct for chromatic aberration.

Huygens built his own compound telescopes, without the benefit of yet to be developed achromatic lenses, that required long distances between the front and rear elements. Newton did not do any further refractive lens development himself. He preferred to work around the problem altogether by using curved first surface reflective mirrors to avoid the aberrations caused by refraction. In fact, he famously declared that chromatic aberration could not be corrected because he failed to consider one could use two types of glass with different refractive properties.

Christiaan Huygens' compound tubeless refracting telescope and Newton's second reflecting telescope.

The first achromatic lens was created in 1733. It used two elements with different refractive indexes to partially correct for color aberrations and allowed refractive telescopes to be made shorter and more functional.

The three element apochromat soon followed, which was an even better improvement over the two element achromat than the achromat had been over the simple lens.

Much of what lensmakers learned correcting for chromatic aberration also had application to the other, monochromatic, optical aberrations inherent in a simple lens.

Once chemical photography emerged in the 19th century as a way to preserve an image projected by a lens, those who made lenses for photographic use took what had been learned earlier in the field of optics, which had mostly been applied to telescopes and the like, and ran with it. A good survey of the developments in photographic lens design, all based on the optical principles discovered in the 17th and 18th centuries discussed above, can be found in the 'History of Photographic Lens Design' article at Wikipedia. (It's far too long and involved to include a summary here.)

In all there are seven "classic" optical aberrations that compound lenses attempt to correct to varying degrees. Note that these aberrations are not the result of imperfections in the construction of lenses, but are due to the nature of light itself as it passes through refractive materials. These aberrations would be present even if those refractive materials were mathematically perfect.

• Defocus (the lowest order which is easily corrected by changing the distance between the lens and the imaging plane)
• Spherical Aberration
• Coma
• Astigmatism
• Field curvature
• Geometric distortion
• Chromatic aberration