Pair of hip roof dormer windows on the Howard Memorial Hall, Letchworth
A dormer is a roofed structure, often containing a window, that projects vertically beyond the plane of a pitched roof. A dormer window (also called dormer) is a form of roof window.
Dormers are commonly used to increase the usable space in a loft and to create window openings in a roof plane. A dormer is often one of the primary elements of a loft conversion. As a prominent element of many buildings, different types of dormer have evolved to complement different styles of architecture. When the structure appears on the spires of churches and cathedrals, it is usually referred to as a lucarne.
The word dormer is derived from the Middle Frenchdormeor, meaning "sleeping room", as dormer windows often provided light and space to attic-level bedrooms.
Also called simply a gabled dormer, this is the most common type. It has a simple pitched roof of two sloping planes, supported by an outward face (any combination of glazed and unglazed materials). It thus includes a triangular section below the roofline, i.e. a gable. It is also known as a dog-house dormer (due to its similar shape).
Also called a hipped dormer, it has a roof composed of three sloping planes that rise from each side of the dormer frame and converge at the ridge—analogous to the hip roof.
Flat roof dormer
The roof of this dormer is a single flat plane approximately horizontal (although usually slightly inclined to allow rain water to run off).
This dormer also has a single flat plane roof, but in this case, it is sloped in the same direction as the principal roof, only at a shallower angle. A shed dormer can provide head room over a larger area than a gabled dormer, but as its roof pitch is shallower than the main roof, it may require a different roof covering.
As opposed to the dormer being set part way up the slope of the roof, this is a dormer whose face is coplanar with (shares the horizontal position of) the face of the wall below. This means that the face of the dormer is essentially a continuation of the wall above the level of the eaves.
Eyebrow, or eyelid dormer
A low and wide dormer with a curved roof and no sides. Instead, the roof covering is gradually curved up and over the dormer in a flattened bell curve.
This can be a dormer that houses a chimney or a dormer that joins one part of a roof to another.
An arched roof dormer, rounded in shape when viewed from front. Popular in Victorian homes, especially in certain areas, like the Southcott-style row-houses called Jellybean Row in St. John's, Newfoundland.
A three-in-one dormer structure composed of two gable dormers connected by a shed dormer in between.
In Vancouver, there are regulations for laneway houses stating the minimum setback of the face of the dormer from the wall below, with exceptions. This is to prevent overshadowing neighbouring yards. 
Dormers are popular in Ulster, and commonly used to create extra space when a loft is converted into a habitable room.