The goal of this work we introduce eight different types of bitopological groups each of which depending on the notions of ij - ¿ - open sets and ij - ¿ - continuous functions . Also we found the relation between these types and we gave some related examples in one side and gave some properties in the other side .Also the notion of bitopological subgroups and the bitopological quotient groups have been given with some new results as well as defining the bitopological product group and proving some new related results .