The Quantum theory
The quantum theory gave an answer to fundamental questions, which were asked at the turn of the century about atomphysics and couldn't be solved by the classical mechanics, introduced by Sir Isaac Newton. A major problem was the discrete (discrete means that not all values are available, or not continuous) character of the atomic spectra: the atom emits only a select group of wavelengths of light.
This phenomenon was explained satisfactory by the new theory, which was introduced as quantum mechanics by Schrödinger, Heisenberg and Born. Their predecessors were Planck and Bohr.
The technical applications of the quantum mechanics are not unimportant. Without this there wouldn't be any transistors, no chips and therefor no computers (no computers=>no internet, scary isn't it). Neither would there be any lasers and therefor no CD player (long live the quantum mechanics!). Without the quantum mechanics the world around us would be very different; these times a life without computers is not thinkeble, we have become what we are with a lot of help of the computer. I'd almost say worship the quantum mechanics, but since the theory is not complete as far as my knowledge reaches, don't.
The quantum mechanics are based on new and intrigue ideas. Physical presentations that seem natural have to be thrown over board. To understand quantum mechanics very good you need to know a lot of math: linear algebra, matrix theory and Fourier analysis.
I don't know wether this is a good start or not, since I do not know a lot about this subject. The course quantumphysics is a second year subject, at the moment I'm a first year student. So you just hang on for a while, eventually it will be available. If not here, then somewhere else.
What to go home?