An athlete starts to run positioning his back towards the Sun once after sunrise and once before sunset. He turns left, right and left again. In which direction is he finally running in both scenarios respectively?

Let's analyze the two scenarios separately:
Scenario 1: After Sunrise (Sun is in the East)

* The athlete starts with his back towards the Sun, so he is running towards the West.
* First turn: Left $\to$ now facing South.
* Second turn: Right $\to$ now facing West.
* Third turn: Left $\to$ now facing South.
* Final direction after sunrise = South.

Scenario 2: Before Sunset (Sun is in the West)

* The athlete starts with his back towards the Sun, so he is running towards the East.
* First turn: Left $\to$ now facing North.
* Second turn: Right $\to$ now facing East.
* Third turn: Left $\to$ now facing North.
* Final direction before sunset = North.

Therefore, the final directions are South – North respectively.