A cutting insert, comprising: an upper face; a lower face; and a side face connecting the upper face and the lower face; wherein cutting edge sets (21, 22, 23, 24, 25) are formed on at least part of an intersecting ridge line portion of the upper face and the side face, wherein each of the cutting edge sets includes a major cutting edge (23, 24, 25), a minor cutting edge, and a connecting cutting edge that connects the major cutting edge and the minor cutting edge, wherein the major cutting edge of one of the cutting edge sets connects to the minor cutting edge of another one of the cutting edge sets, wherein, in a side view, viewing the cutting insert from a direction facing the side face corresponding to the major cutting edges (23, 24, 25), the cutting edges (23, 24, 25) first descend from a certain corner edge toward another adjacent corner edge, and thereafter rise, wherein a minor cutting edge flank (44, 45) that is part of the side face and that corresponds to the minor cutting edge includes a first minor cutting edge flank that connects to the minor cutting edge and that has a clearance angle of 0°, and a second minor cutting edge flank that connects to the first minor cutting edge flank and that has a clearance angle of a negative value, wherein a connecting cutting edge flank (41, 42) that is part of the side face and that corresponds to the connecting cutting edge includes a first connecting cutting edge flank that connects to the connecting cutting edge and that has a clearance angle of 0° or greater, and a second connecting cutting edge flank that connects to the first connecting cutting edge flank and has a clearance angle that is greater than the clearance angle of the first connecting cutting edge flank. an upper face; a lower face; and a side face connecting the upper face and the lower face; wherein cutting edge sets (21, 22, 23, 24, 25) are formed on at least part of an intersecting ridge line portion of the upper face and the side face, wherein each of the cutting edge sets includes a major cutting edge (23, 24, 25), a minor cutting edge, and a connecting cutting edge that connects the major cutting edge and the minor cutting edge, wherein the major cutting edge of one of the cutting edge sets connects to the minor cutting edge of another one of the cutting edge sets, wherein, in a side view, viewing the cutting insert from a direction facing the side face corresponding to the major cutting edges (23, 24, 25), the cutting edges (23, 24, 25) first descend from a certain corner edge toward another adjacent corner edge, and thereafter rise, a major cutting edge (23, 24, 25), a minor cutting edge, and a connecting cutting edge that connects the major cutting edge and the minor cutting edge, wherein the major cutting edge of one of the cutting edge sets connects to the minor cutting edge of another one of the cutting edge sets, wherein, in a side view, viewing the cutting insert from a direction facing the side face corresponding to the major cutting edges (23, 24, 25), the cutting edges (23, 24, 25) first descend from a certain corner edge toward another adjacent corner edge, and thereafter rise, wherein a minor cutting edge flank (44, 45) that is part of the side face and that corresponds to the minor cutting edge includes a first minor cutting edge flank that connects to the minor cutting edge and that has a clearance angle of 0°, and a second minor cutting edge flank that connects to the first minor cutting edge flank and that has a clearance angle of a negative value, a first minor cutting edge flank that connects to the minor cutting edge and that has a clearance angle of 0°, and a second minor cutting edge flank that connects to the first minor cutting edge flank and that has a clearance angle of a negative value, wherein a connecting cutting edge flank (41, 42) that is part of the side face and that corresponds to the connecting cutting edge includes a first connecting cutting edge flank that connects to the connecting cutting edge and that has a clearance angle of 0° or greater, and a second connecting cutting edge flank that connects to the first connecting cutting edge flank and has a clearance angle that is greater than the clearance angle of the first connecting cutting edge flank. a first connecting cutting edge flank that connects to the connecting cutting edge and that has a clearance angle of 0° or greater, and a second connecting cutting edge flank that connects to the first connecting cutting edge flank and has a clearance angle that is greater than the clearance angle of the first connecting cutting edge flank.