The difference between \(S^ 3\) and \(RP^ 3\) is not too great. Therefore it is not surprising that the theory of links in \(RP^ 3\) is somewhat similar to the theory of links in \(S^ 3\). A link in \(RP^ 3\) can be presented by a diagram in \({\mathcal D}^ 2\). The endpoints of arcs of the diagram must be divided into pairs of diametrically opposite points. The author introduces five types of moves of a diagram which are analogous to Reidemeister moves. Two links in \(RP^ 3\) are isotopic if and only if their diagrams can be connected by a sequence of the moves. The Kauffman bracket polynomial and the Jones polynomial have direct generalizations to the case of links in \(RP^ 3\). The author proves an analogue of the Kauffman-Murasugi inequality and the extremal properties of the inequality for alternating diagrams of links in \(RP^ 3\). She suggests also a criterion for an alternating link L in \(RP^ 3\) to be contained in a ball.