Elements of Editing

Order of Shots - The order of shots can be used to communicate emotion to the audience such as short, quick shots can be used to convey scary/ horror-filled moments. It can also be used to help the audience understand the ongoing story/ back story more. For example, movies that use flasbacks after dialogue often do so to explain to the audience things that they might not understand. Additionally, the order of shots in a movie can classify the genre.

Transitions - The most popular transition is a simple "cut". This is where there is a quick process of movement between one scene to the other, it is so quick that the human eye can barely tell and is faster than a single blink. A "cut" is used in many movies of all genres and in most cases, is the only form of transition used throghout the entire film. The second transition is a "fade". This is where the shot dissolves into either black or to the next shot - although it is usually to black first and then the following scene materializes. This shot can communicate a lot of things, for example, a change in season, a change in time or a change in place. The third transition is called a "cross dissolve", this is where the two back-to-back scenes are momentarily superimosed.

The last shot tranistion is called a "wipe", which is where an image is revealed over another horizontally, vertically or diagonally. This shot is usually seen as unprofessional and used in a comedic way. It could also be used to represent moving at a face pace or time passing.

Pace & Rhythm - This is usually used in a narrative context and has two different types of shots. The first is a short duration shot (normally known as quick edits) which convey action. The second are long duration shots which emit intensity or intemacy to the audience.

Additional Research

Parallel Editing - Also known as cross cutting, alternates between two or more sequences that are happening simultaneously but in different locations. An example of parallel editing is in a romance movies, when the man or women is running to the airport as their significant other is about the get on a plane, or the running scene between Alex and Marty in Madagascar.

Match Cut - This is where a cut from one shot to the other is matched by the action that was also in the previous shot. For example, if someone is throwing a punch in the first shot, the shot that is imediately afterwards must be the impact of the punch on the other subject or object.

The best example from this YouTube video is at the 9 second mark with Will Smith. He goes to hit the alien and the second shot is the impact.

Jump Cut - This is usually an abrupt transition from one movie scene to another. An example of this could be someone starting to walk down a hallway and then the next being that same person a little ways down that same hallway.

Soviet Montage Theory -  Montage is French for "assembly" and this theory heavily relies on editing (which is also another French translation for montage). In the 1920s, Lev Kuleshov pitched his idea that editing is a concept in filmmaking - this was later known as the Kuleshov Effect. This editing technique is where, for example, an actor is intercut with various meaningful images...

…he did this in order to show how editing changes a viewer's interpretation of select images/ footage.

Another individual who developed the montage theory is Sergei Eisenstein. Eisenstein's theory is that editing could be used for more than just illustrating a scene, he believed that an idea should be attained through the juxtaposition of two independent shots - this would present an element of "collage" into a product. From this idea, he refined what he called "methods of montage".

These five methods are: 

1. Metric - This is where editing follows a specific number of frames, Eisenstein based this solely on physical nature of time. This meant that one shot cuts immediately to the next shot, this applies for everything, no matter what is happening in either shots. This is done so that there is an emotional reaction from the audience.
2. Rhythmic - This is related to continuity. While this creates visual continuity, it is also used to maintain the pace of the film.
3. Tonal - Tonal Montage is to create emotional meaning; commonly more complex than Metric  and Rhythmic montage.
4. Overtonal - Overtonal is a combination of Metric, Rhythmic and Tonal montage. Used to consolidate their effects on the audience for a more speculative and complicated effect.
5. Intellectual - This is a number of shots that are collected outside of the film to interpret more in-depth meaning.