  This paper is devoted to one of the members of the G\"ottingen triumvirate,
Gau{\ss}, Dirichlet and Riemann. It is the latter to whom I wish to pay
tribute, and especially to his world-famous article of 1859, which he presented
in person at the Berlin Academy upon his election as a corresponding member.
His article, entitled, "Uber die Anzahl der Primzahlen unter einer gegebenen
Gr\"o{\ss}e" ("On the Number of Primes Less Than a Given Magnitude"),
revolutionized mathematics worldwide. Included in the present paper is a
detailed analysis of Riemann's article, including such novel concepts as
analytical continuation in the complex plane; the product formula for entire
functions; and, last but not least, a detailed study of the zeros of the
so-called Riemann zeta function and its close relation to determining the
number of primes up to a given magnitude, i.e., an explicit formula for the
prime counting function.
