All of the following notes are from the book Cinematography: Theory and Practice by Blain Brown. This book helped me to understand the role of Cinematographer a lot more than I did, and it even adds in extra pointers for Directors as well.

Notes

• Selecting the frame is a fundamental act of filmmaking, choosing the fame is a matter of conveying the story, but is also a question of composition, rhythm, and perspective. 
• The lens is a powerful tool of visual storytelling, the ability of optics to alter out perception of the physical world. The most influential aspect of a lens is the focal length: how wide or long it is. A short focal length lens has a wide field of view, and a long focal length lens is like a telescope; it has a narrow field of view.
• Light and colour are some of the most powerful tools in the cinematographers arsenal, when used properly the have the ability to affect people emotionally.
• Establishing is the ability of the camera to reveal or conceal information, conveying important information or background to the audience.
• On a film set, there is no more fundamental collaboration that that of the cinematographer and director.
• The rule of thirds proposes that a useful approximate starting point for any compositional grouping is to place major points of interest in the scene on any of the four intersections of the interior lines.
• The look of a flickering TV is best accomplished with dimmers, actual televisions flickers considerably less than is usually portrayed but the activity helps sell the effect.

Keywords

• Full Shot - indicates that we can see the character from head to toe, it can also refer to objects as well
• Two Shot - any frame that includes two characters
• Medium Shot - is relative to the subject, can see people's expressions, details of how they are dressed, and so on
• Close ups - one of the most important shots, there are a number of variations
• Medium CU - mid chest up
• Choker - from the throat up
• Big Head CU - just from under the chin and giving a bit of 'haircut'
• ECU - usually just mouth and eyes
• Clean Single - shooting someone's CU and don't include any piece of other actor
• Dirty Single - if a little bit of the other actor is included in the CU
• Over the Shoulder - looking over the shoulder of one actor to a medium of CU of the other actor
• Cutaways - any shot of some person or thing in the scene other than the main characters being covered but that is still related to the scene
• Reaction Shot - specific type of CU or medium, when the camera cuts away to an actor reacting to something
• Inserts - an isolated, self contained piece of a larger scene. 
• High Angle - when the camera is above eye height, it seems to dominate the subject
• Low Angle - can make a character seem ominous or foreboding
• Dutch Tilt - used in mystery/suspense films, the camera is off level
• Key Light - the dominant light on people or objects
• Fill Light - light that fills in the shadows not lit by the key light
• Backlight - light that hits a person or objects form behind and above
• Kicker - a light from behind that grazes along an actor's cheek on the fill side
• Sidelight - a light comes from the side, usually dramatic
• Topper - light directly from above
• Hard Light - light from the sun or small lighting source that creates sharp, well-defined shadows
• Soft Light - light from a large source that creates soft, ill-defined shadows or no shadows at all
• Ambient Light - light that just happens to be in a location or overhead light thats just sort of there
• Practicals - actual working prop lights
• High Key - lighting that is bright and fairly shadowless with lots of fill lights
• Low Key - lighting that is dark and shadowy with little or no fill light
• Bounce Light - light that is reflected off something
• Pan - left or right horizontal movement of the camera
• Tilt - up or down movement of the camera without changing the position
• Move In/Move Out - move the dolly towards or away form the action
• Zoom - moves the point of view in or out without moving the camera