Matter composed of the counter-parts of ordinary matter (they're their charge conjugates, i.e., they have the opposite electrical charge and magnetic moment):
Antiprotons instead of protons.
Positrons instead of electrons.
Antineutrons instead of neutrons.

When matter and antimatter collide, both may be annihilated, and other elementary particles, such as photons and pions, are produced.
In 1932 Carl D. Anderson, while studying cosmic rays, discovered the positron, or antielectron, the first known antiparticle.
In 1928 Paul Dirac wrote an equation (the Dirac Equation) that combined special relativity and quantum theory to describe particles moving at high speeds, winning him a Nobel Prize. It suggested that for every particle with a positive charge (the kind we're used to), there exists another particle with a negative charge, called an antiparticle. These pairs of particles are the same but with opposite charges.

These antiparticles, or antimatter were discovered in the 1930s and are continuing to be studied and even produced today. Antimatter can be created by smashing two particles together in a machine called a particle accelerator such as the ones at CERN. Scientists at CERN have created 50,000 antihydrogen atoms. The study of antimatter will reach a new level upon the completion of CERN's Large Hadron Collider (or LHC) to be completed in 2007.

Antimatter releases energy with 100 percent efficiency versus much less efficient forms of energy production like nuclear fission. Although a long way from being harnessed as an energy source, the implications of creating energy from antimatter are intriguing. It could lead to the world's most efficient source of energy or the world's most destructive weapon. Because antimatter by nature is difficult to produce and store it remains to be seen if it will ever be a practical source of energy. In any case, it will be interesting to see what comes of the antimatter experiments when the LHC at CERN is completed.
Star Trek fans will quickly point out that Enterprise and Voyager are propeled using engines fueled by antimatter. Far from being unrealistic, research at Penn state University and NASA Advanced Space Transportation Program (ASTP) is ongoing in order to create the next generation of thrusters utilizing antimatter.

To date, the highest amount of energy can be produced by annihilating antimatter with matter. Chemical reactions at best can provide 1x10^7 joules/kg, nuclear fision 8x10^13 j/kg, and nuclear fusion 3x10^14 j/kg. Matter antimatter annihilation yields 9x10^16 j/kg.

There are many technical obstacles to be addressed. First, the amount of available antimatter in production is not enough, particle accelerators such as the ones found in Fermilab, close to Chicago, and CERN, in Switzerland, produce somewhere between 1 to 10 nanograms of antimatter annually. The process of production typically involve accelerating protons near the speed of light and slamming it into a metal, such as tungsten. Various subatomic particles are produced by this collision, including antiprotons, the simplest form of antimatter. 71 milligrams of antimatter would provide an equal amount of energy that is provided by space shuttle external tank.

The second obstacle is storage. Antimatter can not be stored in normal containers because it will instantly annihilate once antimatter makes contact with matter. One solution is using Penning Trap, a super cold vacuum using electro magnets in order to suspend particles of antimatter. Antielectrons are difficult to store because of their mass, however, antiprotons are stored much more easily. Antimatter storage reaps several benefits, one of which is O15 production, a radioisotope used for Positron Emission Tomography (PET) of the human brain.

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References:

http://www.engr.psu.edu/antimatter/introduction.html
http://science.nasa.gov/headlines/y2000/ast29may%5F1m.htm
http://science.nasa.gov/newhome/headlines/prop12apr99_1.htm

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