a differential equation with given monodromy group. The solution, published in his 1908 article "Riemannian classes of functions with given monodromy group", rests on three formulas that now carry his name, which connect the values taken by a holomorphic function at the boundary of an arc Γ: These formulas are variously called the Plemelj formulae, the Sokhotsky-Plemelj formulae, or sometimes (mainly in German literature) the Plemelj-Sokhotsky Formulae, after the Russian mathematician Yulian Vasilievich Sokhotski (Юлиан Карл Васильевич Сохоцкий) (1842–1927). Based on his methods of solving the Riemann problem he had developed the theory of singular integral equations (MSC (2000) 45-Exx) which was used above all by the Russian school at the head of Nikoloz Muskhelishvili (Николай Иванович Мусхелишвили) (1891–1976). Plemelj contributed significantly to the theory of analytic functions in solving the problem of uniformization of algebraic functions, contributions on formulation of the theorem of analytic extension of designs and treatises in algebra and in number theory. In 1912, Plemelj published a very simple proof of the special case of Fermat's Last Theorem where the exponent, n, is 5. More difficult proofs of this case were first provided by Dirichlet in 1828 and Legendre in 1830. His arrival in Ljubljana in 1919 was seminal for the development of mathematics in Slovenia. As a good teacher he had raised several generations of mathematicians and engineers. His most famous student is Ivan Vidav. After the Second World War Slovenska akademija znanosti in umetnosti (Slovene Academy of Sciences and Arts) (SAZU) had published his three-year course of lectures for students of mathematics: Teorija analitičnih funkcij (The Theory of Analytic Functions), (SAZU, Ljubljana 1953, pp XVI+516), Diferencialne in integralske enačbe. Teorija in uporaba (Differential and Integral Equations. Theory and Application). Plemelj found a formula for a sum of normal derivatives of one-layered potential in the internal or external region. He was pleased also with algebra and number theory, but he had published only few contributions from these fields – for example a book entitled Algebra in teorija števil (Algebra and Number Theory; SAZU, Ljubljana 1962, pp. xiv + 278) which was published abroad as his last work Problemi v smislu Riemanna in Kleina (Problems in the Sense of Riemann and Klein; edition and translation by J. R. M. Radok, "Interscience Tract in Pure and Applied Mathematics", No. 16, Interscience Publishers: John Wiley & Sons, New York, London, Sydney 1964, pp VII+175). This work deals with