Concessive structures (Konzessive Strukturen) are the tools that let you state that an outcome held true despite an obstacle that might have been expected to prevent it — the idea of "although" or "no matter how." You already know obwohl from earlier levels, but the academic and formal register of German commands a far larger arsenal than this single connector, and each tool in it carries a slightly different degree of formality and a different grammatical function — a range that distinguishes journalistic and scientific writing at an advanced level from everyday speech.
The first tool, ungeachtet, is a preposition that always governs the Genitiv case and means "regardless of": Ungeachtet der Risiken setzte er das Projekt fort. Because it is a preposition rather than a conjunction, it introduces only a noun phrase, not a full subordinate clause, which makes it more compact than an equivalent clause would be.
The second group — wenngleich, obgleich, and obschon — functions exactly like obwohl: each introduces a subordinate clause (Nebensatz) in which the verb is pushed to the end. The difference from obwohl is purely one of register, not meaning; obgleich and obschon read as even more formal than wenngleich, and all three appear frequently in academic articles and official reports.
The third tool, so … auch, is structurally quite different: it means "however / no matter how," and it concedes a degree of an adjective or adverb rather than an action itself. Its fixed pattern is so + adjective/adverb + subject + auch + verb, with the adjective itself fronted to the start of the clause: So schwierig die Aufgabe auch sein mag, wir werden sie lösen — "however difficult the task may be, we will solve it."
The fourth tool, dessen ungeachtet, differs from the previous three because it does not link a subordinate clause to a main clause within one sentence; instead it opens a new, fully independent main clause referring back to a separate preceding sentence: Es gab erhebliche Widerstände. Dessen ungeachtet wurde die Reform verabschiedet. Because it opens the main clause, it triggers the familiar Inversion rule: whatever element is fronted to the start of a main clause pushes the conjugated verb into second position, directly before the subject — exactly as with any fronted adverb of time or place.
The essential difference between the two groups, then, is grammatical function: ungeachtet, wenngleich/obgleich/obschon, and so…auch are all tools within a single complex sentence linking a cause to a result at once, while dessen ungeachtet is a textual connector between two separate, consecutive independent sentences, functioning more like trotzdem or dennoch than like a subordinating conjunction.
The most common mistake advanced learners make is treating ungeachtet as a conjunction that introduces a subordinate clause with a delayed verb, when it is in fact a preposition followed directly by a Genitiv noun phrase with no separate verb at all; many also forget the Inversion rule after dessen ungeachtet, writing the subject before the verb by mistake and forgetting that it occupies the first slot of the new main clause, just like any fronted adverbial.