In 1850 and 1851 he studied in Geneva and came into contact with prominent botanists Edmond Boissier and Alphonse Pyrame de Candolle (who offered him the vacant post of curator at his herbarium).

The following year, Müller travelled with Boissier to collect plants in the Alps of Savoy, the valley of Aoste, and Piedmont.

The Swiss Society of Natural Sciences published his first work in 1857, Monographie de la famille des Résédacées, for which he received the Candolle prize and earned a Doctorate of Philosophy from the University of Zurich.

In 1867 he issued the last delivery of the exsiccata series Die Flechten Europas in getrockneten mikroskopisch untersuchten Exemplaren mit Beschreibung und Abbildung ihrer Sporen.

[3] The genus Muellerargia of the family Cucurbitaceae was named in his honor by Alfred Cogniaux,[4] as well as the following species, Psychotria argoviensis Steyerm.