
der Aufstieg
ascent
The movement upward, for example when climbing a mountain or going up stairs.
Der Aufstieg auf den Gipfel dauerte vier Stunden.
The ascent to the summit took four hours.
ascent / rise
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ascent
The movement upward, for example when climbing a mountain or going up stairs.
Der Aufstieg auf den Gipfel dauerte vier Stunden.
The ascent to the summit took four hours.

rise
The improvement of one's own position in a career, society, or a hierarchy.
Sein schneller Aufstieg zum Abteilungsleiter hat alle überrascht.
His rapid rise to department head surprised everyone.

promotion
In sports, the advancement of a team to a higher division or league.
Die Fans feierten den Aufstieg ihrer Mannschaft in die erste Bundesliga.
The fans celebrated their team's promotion to the first Bundesliga.

rise
The gaining of power, influence, or economic importance by a country, company, or movement.
Die Ausstellung dokumentiert den Aufstieg und Fall des Römischen Reiches.
The exhibition documents the rise and fall of the Roman Empire.
'Aufstieg' (ascent / rise) is derived from the separable verb 'aufsteigen' (to ascend / rise) (auf + steigen). It literally describes the process of 'Nach-oben-Steigens' (climbing upward). This basic idea appears in all meanings, whether on a mountain or in a career.
Nach seinem Aufstieg in der Firma hatte er mehr Verantwortung.
After his rise in the company, he had more responsibility.
The adjective 'steil' (steep) is often combined with 'Aufstieg' (ascent / rise), even in figurative meanings. A 'steiler Aufstieg' (steep rise) describes a very fast and impressive development, whether on a mountain or in a career.
Die Band erlebte nach ihrem ersten Hit einen steilen Aufstieg.
The band experienced a steep rise after their first hit.
In the literal meaning, 'Aufstieg' (ascent) is often combined with prepositions that describe the destination. Common are 'der Aufstieg auf (+ Akk.)' (the ascent to/up a summit) for a peak or 'der Aufstieg zu (+ Dat.)' (the ascent to) for a place.
Der Aufstieg auf die Zugspitze ist sehr anspruchsvoll.
The ascent of the Zugspitze is very demanding.
In the context of careers and society, people often speak of 'beruflicher Aufstieg' (career advancement) or 'sozialer Aufstieg' (social mobility / social rise). The target position is indicated with 'zum/zur'.
Ihr beruflicher Aufstieg zur Managerin war beeindruckend.
Her career rise to manager was impressive.
In a sports context, the fixed expression 'der Aufstieg in (+ Akk.)' (promotion to/into) is key. It describes the move to a higher league.
Der Verein feierte den Aufstieg in die zweite Liga.
The club celebrated promotion to the second division.
The phrase 'Aufstieg und Fall' (rise and fall) is a very well-known fixed expression. It is often used to summarize the history of empires, companies, or influential people.
Das Buch beschreibt den Aufstieg und Fall des berühmten Schauspielers.
The book describes the rise and fall of the famous actor.
increase / ascent
Aufstieg refers to movement upward, whereas Anstieg refers to a path or terrain that leads upward. On a mountain hike, Aufstieg is therefore the action, while Anstieg is the uphill section of the route.

Der Aufstieg zum Gipfel dauerte fast drei Stunden.
The ascent to the summit took almost three hours.
Der steile Anstieg zum Gipfel begann direkt hinter der Hütte.
The steep climb to the summit began just behind the hut.