I think every upper level QM book covers the derivation and implications. Merzbacher, Quantum Mechanics, has a lengthy comparison of the Dirac eqn. and Hamiltonian to its non-relativistic cousins. G. Baym, Lectures on Quantum Mechanics, has a very nice description also.
My favorite article on the relation between the Schroedinger, Pauli and Dirac equations is that of Hestenes:
Consistency in the Formulation of the Dirac, Pauli and Schroedinger Theories David Hestenes, J. Math. Phys., 16, 573-584 (1975)
Abstract. Properties of observables in the Pauli and Schroedinger theories and first order relativistic approximations to them are derived from the Dirac theory. They are found to be inconsistent with customary interpretations in many respects. For example, failure to identify the "Darwin term" as the s-state spin-orbit energy in conventional treatments of the hydrogen atom is traced to a failure to distinguish between charge and momentum flow in the theory. Consistency with the Dirac theory is shown to imply that the Schroedinger equation describes not a spinless particle as universally assumed, but a particle in a spin eigenstate. The bearing of spin on the interpretation of the Schroedinger theory discussed. Conservation laws of the Dirac theory are formulated in terms of relative variables, and used to derive virial theorems and the corresponding conservation laws in the Pauli-Schroedinger theory.
My only critique of the above is that from a particle physics point of view, Hestenes puts too much reliance on the details of E&M interactions that are not any more fundamental to the quantum theory than any other interaction.