Sight, Sound and Motion by Herbert Zettl gives a complete account of the aesthetic variables available to manipulate with motion pictures. If you are looking to identify and name basic features of composition, lighting, etc. it’s enlightening. Early editions are available cheaper than the current 7th edition: https://www.amazon.com/Sight-Sound-Motion-Aesthetics-Production/dp/1133307353.
I think the starting point for cinematography is photography... Mastering the still is the first step to developing an eye for scene compositions. In that regard, there was an excellent book that we used in college, <em>Sight, Sound, Motion: Applied Media Aesthetics</em> by Herbert Zettl. It at least goes into the components on a cursory level, before one starts getting into the technical aspects of achieving them with different lenses, lighting, film stock, etc.
It covers all the fundamentals of mise-en-scene/scene comp including rule of thirds, depth of field, depth of focus, depth perspective, lighting, color, blocking, framing, etc.