Cronology

The development of the electromagnetism follow a very interesting historical order we're going to follow, so first of all we're going to list the chronological order of some of the key concepts that we're going to learn on this course.

Now another very important step is to understand in wich part of the physics is located the electromagnetism, so here is a graph of the different fields of physics in relation of the velocities and magnitude of the phenomena the study.

Diagram

Here we can see something curious, the electromagnetism is not located in the graph, and that have an elementary explanation; the electromagnetism is a part of every field of physics. From cosmology to quantum physics and even Newtonian physics, electromagnetism is a part of every one of those fields. That's why electromagnetism is so important and is fundamental to learn it properly.
But that just sounds like the speech that some electromagnetism professor gives to their students on the first day to make them interested in whatever they want to teach, but it's not always something as useful as they may say.
So, what are some real examples of applications of electromagnetism? Let's begin by analyzing how electromagnetism relates to the size and velocity of a system. The electric field is what keeps the electrons in the atomic nucleus, and it's the same in the case for any system with a minimal size and small speed, it's what link atoms in solids, liquids, and even gases together, and it's also crucial on chemical reactions.
When we talk about small systems at very high velocities, electromagnetism is even more interesting and influential. Because now, not only the electric field is very strong, but also the magnetic field is directly related with the velocity of a charged particle, and because most subatomic particles are electrically charged, the magnetic field is also very strong.
Those magnetic fields are crucial on electronics and material physics, which are the base of modern technology, and is the reason you're able to read this right now.
Now, for larger materials at small velocities, while the electric and magnetic forces may be weaker than gravitational forces, they are not negligible, especially because humans and biological entities are very sensitive to the electromagnetic field. So, even relatively low levels of electricity can be very harmful to ecosystems and human beings, especially for telecommunications and the energy industry, but also for all electric infrastructure from generation plants to power outlets in homes.
Finally, at the planetary scale, we have a lot of heavy electromagnetic influenced objects, including the magnetic field of the planets, quasars, and neutron stars, as well as other kinds of magnetic phenomena.