Dear Rifath,

Any elementary book of quantum mechanics containing application of Schroedinger's equation for spherically symmetric potential will give you idea of quantum numbers, n, l, m used in the vector atomic model of the atom. To know how spin quantum number is taken into account, you can read any book of atomic physics.  A book on Perspective of Modern Physics by Aurthor Beiser may also be sufficient for the elementary reading.

Dear Rifath,

Any elementary book of quantum mechanics containing application of Schroedinger's equation for spherically symmetric potential will give you idea of quantum numbers, n, l, m used in the vector atomic model of the atom. To know how spin quantum number is taken into account, you can read any book of atomic physics.  A book on Perspective of Modern Physics by Aurthor Beiser may also be sufficient for the elementary reading.

There are many books available on this subject narrating the topic from various perspectives ( problem solving, derivation & application). For example Albert Messiah's book gives you the theoretical aspects of Quantum Mechanics. For a problem solving perspective, Zettili's book is a good choice in Quantum Mechanics.  If you are interested in how the concept of Orbitals are related Quantum theory, you have Simon & Nichol's book. If You want to go deep into  advanced quantum theory, then the best book to start with is Attila and Zsabo. The books written by Eric Walter Kimball, Water Kauzmann, Dirac and Hartree are still be read as classics in the field. Harrison's book combines electronic structure theory with solid state physics. 

Modern physics by Arthur beiser...............