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.