I am starting to read General Relativity, and from what i have understood, in this theory, time is a derived notion. An event is not associated with a particular time.
But then what is the physical meaning of an event?
And if time is a derived notion, then the four dimensions in our manifold are all spatial?
You are correct in saying a particular event is not associated with a particular time.
This does not mean that time is derived, though. It's just different for observers travelling at different speeds.
An event is just a point in spacetime. Usually, we care about interesting events, like a lightening strike, or an explosion, or a train passing a flare or whatever. The catch is that observers travelling at different speeds will measure events to be in different places in spacetime: either squished closer together or stretched apart. However, events will always be in the same order (both in time and space), and events happen no matter who's looking.
You could see spacetime as a stretchy (4-dimensional!) rubber sheet, and events as dots on the sheet. You can pull at the sheet to change how far apart the dots are, but you can't swap or erase dots. Here, the pulling is analogous to changing reference frame. The behaviour of this sheet at constant velocities is described in Special Relativity.
As for the last point: they're all space-temporal! They're all derived in the sense that they differ between observers (this is called non-invariant), as I said about time above.
I hope this has cleared some things up.
There is no physical meaning associated to an event. An event is a point in the spacetime manifold, where the manifold itself is a mathematical structure allowing to retrieve the effect of gravity as seen by an arbitrary observer.
To say it otherwise: any observer will see spacetime as split between space and time, which means that no observer sees an event per se. If we call physics the modelling of what we can observe, an event is not physically meaningful - it is more a mathematical tool.
In GR we describe different systems in the Universe or the Universe as a whole using four coordinates, namely three position coordinates and one time coordinate. A certain point in this four-dimensional space (pseudo-Riemannian manifold to be more precise) we call an event. Some fixed time is therefore not what we usually call an event since different for a fixed time one could have different position coordinates.
The physical meaning of an event is therefore based on the union of space and time. This was the main idea of Einstein and this union was called spacetime. An event in GR is therefore a point in spacetime whereas in Newtonian theory we had time as an event since time and position where considered differently and separately.
In GR we always deal with three spatial coordinates and one time coordinate. Of course one could regard time as a special spatial coordinate that changes the metric to a non-positive definite metric, but of course we like to give it a physical meaning.
Note: we do not always describe a system in GR with one time and three spatial coordinates. I chose to the basic approach to explain it. As described below there are exceptions to this.
