Re-Learning the Theories of Electricity and Magnatism

I am now in the process of changing from Engineer to Physicist. So, and reviewing a lot of my physics. It'll be a long road, and I will being going back to undergrad to do it. 

The laws of mechanics are straight forward enough.

Newton's second law:

Which is equivalent to the basic law in Lagrangian Mechanics:

Which is in-turn equivalent to the basic law's in Hamiltonian Mechanics:

Certainly, there are a lot of special cases to consider, the work energy theorem, the notion of conservative forces, etc. --I need plenty of practice, in addition.

But I will now focus on Electricity and magnetism, since it is used as a model to thing about many of the big problems in physics.  

The laws themselves are plenty....

There are the four equations for free charges:

Then the two new equations for total charge:

Beyond that each one has an integral form:

Beyond that, we need to comrehend that:

There is all that funkiness with the units of current density,  magnetizing field, electric displacement field, electric field, and magnetic field.  The accounting for that is something I don't have straight yet--not even conceptually.  

Mathematically, I need to review the meaning of the div and curl, as well as integrating over lines and surfaces. 

Beyond that, there is the task of learning how special relativity plays into things, and learning the covariant formlation of clasical electromagnatism.  But I suppose the last part can come while I try to tackle special relativity in full-form. 

So much to learn and so little time.