  Unlike the classical theory of Fourier series which deals with decomposition
of a function into sinusoidal waves the Vilenkin (Walsh) functions are
rectangular waves. The development of the theory of Vilenkin-Fourier series has
been strongly influenced by the classical theory of trigonometric series but
there are a lot of differences also. The aim of my master thesis is to discuss,
develop and apply the newest developments of this fascinating theory connected
to modern harmonic analysis. In particular, we investigate N\"orlund means but
only in the case when their coefficients are monotone and prove convergence in
Lebesgue and Vilenkin-Lebesgue points. Since almost everywhere points are
Lebesgue and Vilenkin-Lebesgue points for any integrable functions we obtain
almost everywhere convergence of such summability methods.
