Questions & Answers about Я оставил заявку на курс русского языка.
Yes, оставить often means to leave something somewhere, but in some contexts it also means to leave behind / submit / provide.
In оставил заявку, the idea is I left/submitted an application. This is a normal Russian way to say that someone filled in or sent in a request/application, especially online or by phone.
So here оставил заявку is best understood as submitted an application / left a request.
That is the marker of the past tense in Russian.
The infinitive is оставить.
To form the past tense, Russian usually replaces -ть with -л:
- оставить → оставил = left / submitted
- делать → делал = did / was doing
In this sentence, оставил means submitted / left in the past.