
trotz
despite
As a preposition with the genitive (also dative in colloquial speech) that indicates a counter-reason; 'although'.
Trotz des starken Regens fand das Fußballspiel statt.
Despite the heavy rain, the soccer game took place.
despite
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despite
As a preposition with the genitive (also dative in colloquial speech) that indicates a counter-reason; 'although'.
Trotz des starken Regens fand das Fußballspiel statt.
Despite the heavy rain, the soccer game took place.

despite everything
A fixed expression meaning 'regardless of all difficulties' or 'nevertheless'.
Die Reise war anstrengend, aber trotz allem ein unvergessliches Erlebnis.
The trip was exhausting, but despite everything, it was an unforgettable experience.
The preposition 'trotz' (despite) is related to the noun 'der Trotz' (defiance), which means 'resistance' or 'stubbornness'. So you can imagine 'trotz des Wetters' (despite the weather) as 'in resistance to the weather'.
Aus reinem Trotz hörte das Kind nicht auf zu schreien.
Out of pure defiance, the child did not stop screaming.
Although the genitive after 'trotz' (despite) is considered correct in standard German, the dative is used in everyday language and often in written language as well. Both forms are very common.
Trotz des schlechten Wetters machen wir einen Spaziergang. (Genitiv)
Despite the bad weather, we're going for a walk. (genitive)
The expression 'trotz allem' (despite everything) often appears at the beginning of a sentence and introduces a main clause in which the verb follows directly (position 2). It summarizes previously mentioned difficulties.
Es gab viele Probleme bei der Planung. Trotz allem war die Feier ein großer Erfolg.
There were many problems with the planning. Despite everything, the celebration was a great success.
although
Obwohl and trotz introduce a counter-reason that does not prevent the result. Obwohl introduces a subordinate clause with a verb; trotz is a preposition placed before a noun phrase. The meaning can remain the same; only the sentence structure changes.

Trotz des starken Regens gehen wir spazieren.
Despite the heavy rain, we are going for a walk.
Obwohl es stark regnet, gehen wir spazieren.
Although it is raining heavily, we are going for a walk.