The beginning of the twentieth century was a particularly  active period for physics.

In 1905 Albert Einstein proposed the theory of Special Relativity and Werner Heisenberg invented the theory of Quantum  Mechanics, but this last theory was not relativistic.

In 1928 the British physicist Paul Dirac solved this problem by proposing an equation that combined Quantum Mechanics with special relativity. But this equation seemed to have a problem: it foresaw one electron with positive energy and one with negative energy. But in classical theories the energy of a particle has to be always positive. Then Dirac hypothesized that all states with negative energy were occupied, and that the transition of one particle with negative energy to positive energy lead to the "creation" of a pair of particles: the particle with positive energy and the hole left in the states with negative energies, which he referred to as an antiparticle.

Later Dirac asked himself what the antiparticle of the electron could be and he slowly came up with the idea that to any particle corresponded an antiparticle, with the same mass, but opposite electric charge. In particular, the partner of the electron is the antielectron, identical to the electron but with a positive charge. In his Nobel Lecture Dirac speculated on the possible existence of a new Universe, made of antimatter!

But physics is an experimental science and all theoretical predictions have to be verified by experiments; in other words, we should observe the antielectron experimentally.

Fig 2: Carl D. Anderson, Nobel Prize for Physics (1936).

In 1932 the American physicist Carl David Anderson observed in Cosmic Rays a particle which behaved like an electron, but which had a positive charge: he had discovered the first antiparticle, the antielectron, also called a positron.

In order to discover the antiproton, scientists had to wait for the new powerful particle accelerators, which could accelerate protons or electrons to very high energies. In the 50's a new accelerator in Berkeley, California reached energies sufficient to produce antiprotons and antineutrons, which were observed with sophisticated equipment.
In the following years new accelerators at CERN, Geneva, and  Brookhaven, USA, made possible the production and observation of the antideuteron. Later, even higher energy accelerators at Serpukhov, Soviet Union, and at CERN allowed scientists to produce and observe antihelium 3 and antitritium.

Recently, anti-atoms of anti-hydrogen  (anti-H=anti-p + e⁺) were produced at CERN decelerating antiprotons and antielectrons kept trapped in a vacuum via magnetic fields. It is more difficult to trap anti-hydrogen atoms because they are neutral: most of them hit the walls of the trapping chamber where they annihilate with the ordinary atoms of normal matter.