By this time I certainly hope that you are familiar with the two postulates, due to Einstein, that lead to the theory of special relativity. They are:
Properly speaking, the second postulate is a consequence of the first, since if the speed of light depended on the motion of its source the laws of electrodynamics (which determine the speed of freely propagating electromagnetic waves) would depend on the inertial frame of the source, which contradicts the first postulate. For what it is worth, the first is not as obviously a consequence of the second: it seems entirely possible for some laws to depend on the velocity of the source and not contradict the second postulate, as long as they are not electrodynamical in nature. This has been the subject of considerable discussion, and I hesitate to state a religious view upon it.
I will, however, point out that in the opinion of Dirac, at least -- the discovery of the uniform 3K blackbody background explicitly contradicted the first postulate but not the second. You might amuse yourself, some quiet evening, by considering experiments that would measure your absolute velocity relative to the ``rest'' frame of this radiation. The second postulate (which is all we need) thus seems to be the safer of the two upon which to base our reasoning.
I strongly recommend that you read J11.1 -- J11.2 on your own. They are ``true facts'' that will come in handy some day, and should astound and amaze you. Yes, Virginia, special relativity really really works.
For our purposes, we will begin with a brief review of the basic Lorentz transformation and an introduction to four vectors. Because we will do it again (correctly) in a week or so we won't take long now. We will also study four-velocity and four-momentum. This will suffice to give us the ``flavor'' of the theory and establish the geometricaly grounds for the matrix theory we will then derive.
As an application of this, we will study Thomas precession briefly and then go on to perform a detailed application of the theory to the dynamics of interacting charged particles and fields. We will spend the rest of the semester on this subject, in one form or another.