If you're looking for a very academic "perfect world" approach to project management and a good starting place to build a learning foundation from, I would start with the Project Management Body of Knowledge (PMBOK). It's the foundation of the Project Management Professional (PMP) certification.
The PMBOK is useful mainly for passing the PMP. It will introduce you to a lot of the language you will hear regarding project management but I am yet to work on a project which follows the rigid practice defined in the PMP. However, that's if you can get through more than 2 chapters without falling into a deep coma.
To RG's point, you are probably better off requesting to manage a small project at work so you can get familiar with how it's done. Creating/using a project schedule (and knowing the critical path), milestone payments, design review gates etc. are much more meaningful if you participate in them.
Alternately, there are some free online courses you can take that will teach you what you need to know to get started as a PM. Here's a couple:
The best way to learn is running a project. Get the big bottle of Excedrin because there will be a lot of headaches from either incompetence, poor planning or someone dragging either feet. Good luck.