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In earlier works, D(1) (arXiv:0709.1515 [math.AG]), D(11.1) (arXiv:1406.0929[math.DG]), D(11.2) (arXiv:1412.0771 [hep-th]), and D(11.3.1) (arXiv:1508.02347[math.DG]), we have explained why a D-brane in string theory, when treated as afundamental dynamical object, can be described by a map $\varphi$ from anAzumaya/matrix manifold $X^{Az}$ (cf. D-brane world-volume) with a fundamentalmodule with a connection $(E,\nabla)$ (cf. Chan-Paton bundle) to the targetspace-time $Y$. In this sequel, we construct a non-Abelian Dirac-Born-Infeldaction functional $S_{DBI}^{(\Phi, g, B)}(\varphi,\nabla)$ for such pairs$(\varphi,\nabla)$. We next develop a technical tool needed to study variationsof this action and apply it to derive the first variation $\deltaS_{DBI}^{(\Phi,g,B)}/\delta(\varphi,\nabla)$ of $S_{DBI}^{(\Phi,g,B)}$ withrespect to $(\varphi,\nabla)$. The equations of motion that govern the dynamicsof D-branes then follow. A complete action for a D-brane world-volume mustinclude also the Chern-Simons/Wess-Zumino term$S_{CS/WZ}^{(C)}(\varphi,\nabla)$ that governs how the D-brane world-volumecouples with the Ramond-Ramond fields $C$ on $Y$. In the current notes, aversion $S^{(C,B)}_{CS/WZ}(\varphi,\nabla)$ of non-AbelianChern-Simons/Wess-Zumino action functional for $(\varphi,\nabla)$ that followsthe same guide with which we construct $S^{(\Phi,g,B)}_{DBI}(\varphi,\nabla)$is constructed for lower-dimensional D-branes (i.e. D(-1)-, D0-, D1-,D2-branes). Its first variation $\deltaS^{(C,B)}_{CS/WZ}(\varphi,\nabla)/\delta(\varphi,\nabla)$ is derived and itscontribution to the equations of motion for $(\varphi, \nabla)$ follows. Thecurrent notes lay down a foundation toward the dynamics of D-branes along theline of this D-project.

Dynamics of D-branes I. The non-Abelian Dirac-Born-Infeld action, its  first variation, and the equations of motion for D-branes --- with remarks on  the non-Abelian Chern-Simons/Wess-Zumino term