Action of topological group and topological groupoid

Our main goal in this paper is to study the topological group and topological groupoid. We concentrated to research the relation between topological groupoid and topological group. We define actions of topological group and define Ehresmann groupoid. We give symmetry between principal actions law of topological groupoid and the principal action law of topological group on a topological space using groupoid Ehresmann. We connected between continuous action and free action. We define a new kind of groupoid which are D-groupoid and SD-groupoid. The condition of D-groupoid are weaker than the condition of principal groupoid, so we used D-groupoid instead of groupoid principal and we get the same result. We study some types of topological groupoid and we give some results of action of topological group on the lookout proposition.