Around the turn of the century, the German physicist Max Planck postulated that a black body emitted light in discrete packets of energy. A few years later in 1905, Einstein invented the concept of light quanta by which he explained the photoelectric effect (and for which he recieved the 1921 Nobel Prize). The next twenty years were filled with revolutionary ideas. Niels Bohr postulated that electrons orbiting atoms could do so only in a discrete set of orbits, and Louis de Broglie proposed the idea that not only did light, previously thought to be a wave, have particle properties, but all particles had wave properties. The cumulation of all this was the theory of Quantum Mechanics, developed in the mid twenties by Erwin Schroedinger, Werner Heisenberg and Paul Dirac.
Quantum Mechanics describes all of the microscopic world of atoms, electrons ..... (this definitely needs to be worked out more!
A nice parting quote attributed to Niels Bohr:
If anyone says he can think about quantum problems without getting giddy, that only shows that he has not understood the frist thing about them
Ard Louis, email@example.com