Like the guitar, the mandolin is a poorly sustaining instrument --- a note cannot be maintained for an arbitrary time as with a violin. Its higher pitch makes this problem more severe than with the guitar, and as a result use of tremolo (rapid picking on a single note) is commonplace.
Mandolins come in a few forms. The more traditional roundback has a vaulted back made of a number of strips of wood in a bowl formation, similar to a lute. The flatback mandolin derives from the cittern. The carved top instrument was introduced by the Gibson company. These use the best of violin making techniques and guitar making production.
Two of the most common carved top flat-backed mandolins are the F-style, which has a scroll near the neck, and points on the sides; and the A-style, which is round or pear shaped and has no points. These styles can also have either f-shaped soundholes, like the violin family, or an oval sound hole under the strings. Naturally there is much variation among makers, and styles other than these exist as well, but these are the most common. The F-hole, F-style mandolins are considered the most typical and traditional for bluegrass, while A-style with oval hole is more for Irish music.
Larger versions of the mandolin are the mandola (a fifth below the mandolin, as the viola is below the violin), the octave mandolin (an octave below the mandolin), and the mandocello, which is tuned an octave plus a fifth below the mandolin (like a cello). All of these have 8 strings tuned in unison.