The forgotten topological index of a graph [Formula: see text] is defined as the sum of weights [Formula: see text] over all edges [Formula: see text] of [Formula: see text], where [Formula: see text] and [Formula: see text] are the degrees of the vertices [Formula: see text] and [Formula: see text] in [Formula: see text], respectively. In this paper, we characterize the extremal properties of the F-index (forgotten topological index). We first introduce some graph transformations which increase or decrease this index. Furthermore, we will determine the extremal acyclic, unicyclic and bicyclic graphs with minimum and maximum of the F-index by a unified method, respectively. Recently, Akhter et al. [S. Akhter, M. Imran and M. R. Farahani, Extremal unicyclic and bicyclic graphs with respect to the F-index, AKCE Int. J. Graphs Comb. 14 (2017) 80–91] characterized the extremal graph of unicyclic and bicyclic graphs with minimum of the F-index. We will provide a shorter proof.