Antimatter was discovered in 1932, by the American physicist Carl David Anderson.
Anderson was observing the tracks produced by cosmic rays in a cloud chamber (a chamber where moving charged particles produce visible tracks). Some of the tracks produced were similar to those that would be produced by electrons , but when a magnetic field was placed in the chamber, the particles deflected in the direction that a positively charged particle would.
What did this mean?
Anderson realised that a new particle was produced. It had the same mass and charge as the electron, but the charge was of the opposite sign.
It became known as the anti-particle of the electron and was named the positron.
We now know that each particle has an anti-particle. We usually denote an anti-particle with the same symbol as the particle with a bar over it.
History of Antimatter:
English physicist Paul Dirac predicted mathematically the existence of positrons and other anti-particles, in the late 1920's
The existance of anti-protons and anti-neutrons was confirmed experimentally in 1955
Since then, the full range of anti-particles has been confirmed.