The concept of near polygon was introduced by \textit{E. Shult} and \textit{A. Yanushka} [Geom. Dedicata 9, 1-72 (1980; Zbl 0433.51008)] as a tool in the study of systems of lines in a Euclidean space. In this paper, the authors construct some infinite families of near polygons, and classify near hexagons with lines of length 3 and with quads. This paper is a compilation of three reports [\textit{A. E. Brouwer}, `The classification of near hexagons with lines of size three', Report R 85-16, Instit. f. Elektroniske Systemer, Aalborg/DK (Sept. 1985); \textit{A. E. Brouwer}, \textit{A. M. Cohen} and \textit{H. A. Wilbrink}, `Near polygons with lines of size three and Fisher spaces', Math. Centr. Report ZW 191, Amsterdam (May 1983); and \textit{A. E. Brouwer} and \textit{H. A. Wilbrink}, Geom. Dedicata 14, 145-176 (1983; Zbl 0521.51013)]. The third author was referee of the second report mentioned above.