well it depends on what you mean by project management, I have trained and have been certified in Agile (DSDM) Prince (Practitioner) and as a PMP (PMI) - PMBOK
Agile is dancing around its good for light projects common in software but you still need to have controls in place despite what many developers want
Prince is focused on the Business side with stage boundaries are big thing and organisational structure but is really lacking on how to do stuff
PMI is quite technical
All of the above will fail if treated as a prescriptive solution all should be tweaked to suit what you are doing
Project management is many things but the three core things are
you need to lead
you need to organise
You need to have a plan
There more tools out there than you can shake a stick at... many are just list tools - you can do this with any list tool even excel or note pad, the next level up is something that uses pert and does some resource scheduling accounting etc MS Project is a tool that can be used for small medium and some slightly larger projects (there is an open source equivalent that is probably good for small and medium sized projects
https://openproj.en.uptodown.com/windows
If you dont have a large budget large team etc etc in all honesty a list or very basic tool will more often than not suffice