Polygonal number is a positive integer which can be presented as dots (or other figures) arranged in the form of a regular polygon which is built starting from a vertex of such a polygon and adding layers on nonadjacent sides. Central polygonal numbers are positive integers which can be represented by grouping dots around a fixed point. In the first part of this graduation thesis the simplest polygonal and central polygonal numbers are explicitly described. Algebraic formulas for \(n-\)th \(m-\)gonal number are found and these formulas are interpreted geometrically. Relations between polygonal numbers of different orders are derived. The second part of this thesis examines multipolygonal numbers, i.e. numbers which are polygonal in more than one way. Double multipolygonality is studied in more detail. Some results on Pell and Pellian equation are given and these results are used for determining \((n,m)\)-gonal numbers, i.e. number which are simultaneously \(n-\)gonal and \(m-\)gonal. The problem of determining numbers which are polygonal in three or more ways is quite complicated, so the sole result of this kind that is reported in this thesis is that the only \((3,4,5)\)-gonal number is 1.