The invention relates to a panoramic attachment optical system and a panoramic optical system for taking an image having a full 360.degree.-direction angle of view or projecting an image at a full 360.degree.-direction angle of view. These optical systems are reduced in size and flare light and improved in resolving power. A panoramic attachment optical system 10 attached to the entrance side of an image-formation lens 20 to form a full 360.degree.-direction image on an image plane 30 comprises a transparent medium that is rotationally symmetric about a center axis 1 and includes at least two internal reflecting surfaces 12, 13 and at least two refracting surfaces 11, 14. A light beam enters the transparent medium via the refracting surface 11, and reflects at the internal reflecting surfaces 12 and 13 in this order to leave the transparent medium via the refracting surface 14, forming an image at a position of the image plane 30 off the center axis 1 via an image-formation lens 20. The internal reflecting surfaces and the refracting surfaces are each of shape rotationally symmetric about the center axis 1, and a light beam 2 coming from far way forms an image at least one time.