The camera lens is a projection lens. Such a design gathers the image-forming light waves that emanate from the subject. The larger the working diameter of the lens, the more light that will be gathered, the brighter the resulting image. The lens is constructed using a transparent material like glass or plastic. The shape resembles a lentil seed, hence the name “lens”. The classic shape is convex, meaning the lens bulges outward, making it thicker in the middle. This shape forces the Light rays from the subject to strike the lens at different angles. As these rays transverse the lens, the direction of their path is changed. This path change is called “refraction”.
The refracted light rays are caused to bend inward. We can trace their revised path; it resembles a cone shape. If we position a ground glass viewing screen or film or image sensor at the apex of this cone of light, a focused image is revealed.
If the lens design is a solitary (one element) convex lens, the resulting image will be degraded. Now we are talking about the seven aberrations (lens defects) that plague. Over the years, we have learned to mitigate each. This is accomplished by constructing a complex lens. This is a multi-element design. Each element has a different shape; some are convex, some are concave, some are cemented together, and some are air spaced. Such a complex array is necessary to force the image forming rays to come to a precise focus at the apex of the cone.
Additionally, twin lens designs and single lens designs each have idiosyncrasies. Now the optician chooses shapes and materials that best work for the task at hand. Suppose a wide-angle lens is tasked to be fitted to a single lens reflex body. A wide-angle must have a short cone of light (short focal length). This is a problem, because a reflex design imposes a moving mirror between the lens and film/sensor. Now the optician must somehow elongate the cone and still retain the wide-angle effect. Retro-focus to the rescue! The optician fits a backwards telephoto. Ever look through a telescope backwards? The view is wide-angle. This design elongates the image forming rays allowing space for a mirror and shutter.
The optician has many tricks up his/her sleeve. A telephoto is a long focal length lens. If the barrel remains long, using the camera will be awkward. The optician shifts the focal length measuring point (rear nodal) forward. This design shortens the barrel length.
To answer your question: Basically all cameras lenses and constructed around a simple singe element convex lens design. Because such a design is wanting as to image quality, the optician add lenses of various shapes to mitigate aberrations and to custom fit the lens to the task at hand.