Quantum mechanics is exceptionally difficult from a mathematical point of view. From a conceptual point of view though, it is relatively simple to gain a basic understanding. The basis of quantum mechanics is:
1. All matter is particle and wave like, but only ever displays one or the other property, depending on what experiment we perform.
2. All energy, mass, and time is divided into discrete units, or quanta, that must be a multiple of a certain number (Planck’s Constant).
3. The greater accuracy with which you measure the location of a particle, the less you are able to measure about its velocity (Heisenberg’s Uncertainty Principle). This means that every particle is not at a finite point, but spread out in space according to its probability function.
4. No two particles can be in the same state at the same time. State is a combination of quantum properties such as spatial location, temporal location, and spin number.
5. All observed particles obey either Bose-Einstein statistics (and are so called Bosons) or Fermi-Dirac statistics (and are so called Fermions).
Those are the main principles, but of course you can study it to the point of the cutting-edge physicists if you want to devote your life to it. What I have listed is imperfect, because in quantum there is very little certainty about anything, and its very nature makes blanket rules difficult. Hope this helps.