The simplest is the lean to or shed which has only one slope a roof with two slopes that form an a or triangle is called a gable or pitched roof this type of roof was used as early as the temples of ancient greece and has been a staple of domestic architecture in northern europe and the americas for many centuries.
Unusual pitched roofs.
Mansard roof this roof is also known as a french roof and the sides come down and meet a low pitched roof.
The upper portion of the roof is heavily pitched and the lower slope is gently pitched.
A lean to roof similar to a skillion roof is composed of one angled pitch.
The term gable refers to the triangle spot that is formed when the two pitched areas of the roof meet.
As pictured above it is likely to extend much further than a mansard besides having the lower pitched slope on the bottom.
You could extend the roof of your home out in one continuous piece or you could attach it at a different level to give your roof a stepped look.
Roof terminology is also not rigidly defined.
Consider making your roof large enough to cover multiple living areas and uses.
These types of roofs are unusual but offer plenty of interior space for an attic.
The roof is supported at one end by a wall raised higher than the other enabling the roof to be pitched at a steeper angle to allow runoff in heavy rain.
This style traditionally includes extra living space with dormers inserted along the roof to bring light into the uppermost living area or attic.
It is a complex framing style that can be or usually is a variation of the hip roof but a gable home may also make use of bonnet frame.