The invention relates to a panoramic attachment optical system and a panoramic optical system for taking an image having a full 360°-direction angle of view or projecting an image at a full 360°-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°-direction image on an image plane 30 comprises a transparent medium that is rotationally symmetric about a center axis 1 and includes at least one internal reflecting surface 12 and at least two refracting surfaces 11 and 13. A light beam incident on the entrance surface 11 in order of travel of light enters the transparent medium via the entrance surface 11, and is reflected at the internal reflecting surface 12 to leave the transparent medium via the exit surface 13, forming an image at a position of the image plane 30 off the center axis 1 via the image-formation lens 20. The internal reflecting surface 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 in a section including the center axis 1, but does not form any image in a plane that is orthogonal to that section and includes a center ray 20 of that light beam.