The battery instruments are what most people commonly refer to simply as drums. (For brevity's sake, these descriptions will not pertain to the numerous types of hand drums, both mass-produced and otherwise such as congas, djembes, dumbeks etc. and instead will focus on the orchestral and drumset type instruments.) Most drums have only 1 or 2 heads, usually made of calf, goat, or synthetics which are most common and include plastics, kevlars, and mylars. Shell types are equally variable, with plastics, woods, and metals all being common.
They are usually cylindrical in shape, with the exception of timpani bowls which come in various parabolic and non-parabolic shapes. Hardware, or any part of the drum that doesn't function in a direct musical sense, also comes in a large cornucopia of varieties. Sizes are stated with the depth first usually, and the head diameter second. For snare drum, common ones are 5"x14" ; 6.5"x14" ; 3"x13" ; 11"x13" (marching). For bass drums, usually an 18"x36" drum is good for general ensemble use. Tenor drums, tom-toms, and other drums come in various diameters and widths, too numerous to describe in detail here. The timpani (timpano is singular) are measured by diameter only since the bowls are not cylindrical. A standard set of five drums include 32", 29", 26", 23", and 21" timpani which each have a <1 octave range. The set of drums though, covers at least C-a1.
Heads
Weights, thicknesses, and colors are all possible variables in the selection of a drumhead and this is one of the most crucial parts to the sounds sf any drum. Many orchestral percussionists prefer calf heads on their drums for the warmest, truest sounds. Calf, and other organic heads, are very susceptible to changes in weather so it is imperative that one lives in a climate suitable for the use of calf heads (see the timpano picture for a calf head). If one does not, it is important to know how to properly care for a head on stage and off (wetting, drying, heating etc). Calf heads generally are more forgiving to the imperfections in drums, and since organic, will conform to the problematic areas on the bearing edge and elsewhere (out-of-round drums etc.). Plastic drumheads far outnumber calf heads mainly due to price and upkeep needs. The trend as of late has been for companies to try to recreate calf sounds synthetically with head series such as Remo's ™Fiberskyn and ™Renaissance lines.
Hardware
The majority of hardware on a drum is there for the purpose of holding the head in tension via the counterhoop(s). Snare drums generally have considerably more hardware than bass drums or tenor drums since they need a mechanism to hold the snares in on and off positions. Snare units 
can come in different sizes and types, common ones being gut, steel, wire, plastic, and cable. These units control tension horizontally, and vertically, as well as the on-off capacities that all throwoffs (the hardware which contains the switch for on and off) have. Timpani probably have the most hardware as one can see in this picture. The pedal mechanism on this timpano is a locking-clutch system (as opposed to the Ludwig style in which the balanced-action pedals do not lock in place). The precise vertical movement of the counter hoop is essential for this instruments tunability and clarity of pitch. An incredible amount of tension is pent up inside the hardware and therefore, any undesired collision with the counterhoop, or any other part, can have severe effects on the seating of the head.
Sticks and Mallets
As with all the other characteristics of percussion, these also come in various forms - metal, wood, and synthetic. Most people use wood sticks for just about any playing situation. Brushes are also used frequently on snare drums, and can provide interesting textures for the jazz drumset artist especially. Sometimes cloth covered sticks are used for special effects, such as on Bartok's Concerto for Orchestra in which some players wrap wood sticks with leather to get a warmer tone with more fundamental and less overtones (this excerpt also requires the snares to be off). Bass drum and timpani mallets come in many sizes and types with a wool-covered being the most popular. Shafts are made from metal, bamboo, and wood with cores ranging from wood, plastic, and felt.
