Quantum Numbers Tutorial + Practice Problems Explained [Complete Lesson]: Crash Chemistry Academy 

basic tutorial for quantum numbers along with practice problems.
-More on Quantum Numbers: Wikipedia-
Quantum numbers describe values of conserved quantities in the dynamics of a quantum system. In the case of quantum numbers of electrons, they can be defined as "the sets of numerical values which give acceptable solutions to the Schrödinger wave equation for the hydrogen atom". An important aspect of quantum mechanics is the quantization of observable quantities, since quantum numbers are discrete sets of integers or half-integers, although they could approach infinity in some cases. This is distinguished from classical mechanics where the values can range continuously. Quantum numbers often describe specifically the energy levels of electrons in atoms, but other possibilities include angular momentum, spin, etc. Any quantum system can have one or more quantum numbers; it is thus difficult to list all possible quantum numbers.
How many quantum numbers?
The question of how many quantum numbers are needed to describe any given system has no universal answer. Hence for each system one must find the answer for a full analysis of the system. A quantized system requires at least one quantum number. The dynamics of any quantum system are described by a quantum Hamiltonian, H. There is one quantum number of the system corresponding to the energy, i.e., the eigenvalue of the Hamiltonian. There is also one quantum number for each operator O that commutes with the Hamiltonian. These are all the quantum numbers that the system can have. Note that the operators O defining the quantum numbers should be independent of each other. Often, there is more than one way to choose a set of independent operators. Consequently, in different situations different sets of quantum numbers may be used for the description of the same system.
Wikipedia contributors. "Quantum number." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 27 May. 2016. Web. 30 May. 2016.