In this thesis we study incidence algebras. At the beginning, we define a partially ordered set, local finiteness of a partially ordered set and give several examples. After that we introduce the concept of incidence algebra of a locally finite partially ordered set over a commutative ring R with identity. It is shown that the incidence algebra is an associative R-algebra with identity and that it can be embedded into the algebra of triangular matrices. The central part of the thesis deals with the calculation of the Moebius function on the elements of a partially ordered set and with the generalized formulas of Moebius inversion. Applications of Moebius inversion are illustrated by examples from combinatorics. In addition, we define the concept of E-functions in an incidence algebra, where E is an equivalence relation, and we show the connection between the incidence algebra and the set of all E-functions in it.The concept of reduced incidence algebra is introduced and a characterization of the reduced incidence subalgebra of a finite partially ordered set over a field is given. Finally, we give examples that show connections between reduced incidence subalgebras and rings of formal power series.