The paper is based on extensive research carried out on students of mathematics who had completed a university course of calculus. The basic purpose of the research was to determine the students' images of the concept of limit, that is to find out their associations, conceptions and intuitions connected with limits and to determine the degree of their efficiency and the sources of their formation. To achieve the objectives an expanded set of selected problems--simple but not quite standard--and various other research instruments were used. Several classes of images of the limit concept have been identified and described, according to their main foci: neighborhoods, graph approaching, values approaching, being defined at x[subscript 0], limit of f atx[subscript 0] equals f(x[subscript 0]), and algorithms.