The study on signed graphs have been one of the hot research fields in the past few years. Theories on ordinary graphs have been generalized to signed graphs in many major aspects, such as the areas of flows, circuit covers, homomorphisms and so on. Graph colorings theory, which is strongly related to these aspects, has a central position in discrete mathematics.However, there are very few knowledges known on colorings of signed graphs so far. The thesis is devoted to generalize a series of concepts, results and methods on vertex colorings of graphs to signed graphs for the first time. In particular, we introduce the notions of circular colorings and related integer colorings and list colorings for signed graphs.Some fundamental results for each notion are proved. Analogues of some classical results like Brooks' Theorem and Haj\'