In this talk, we introduce basic concepts and some special solutions of incompressible Euler equations. First, we present relations between three key elements of the Euler equations; velocity, vorticity, and the flow map. Then we introduce a special type of solution of the Euler equations in 2D called a vortex patch and its related works on stability. Finally, we present axisymmetric solution without swirl in 3D and its associated results on global regularity.