A transformer and discharge lamp lighting device are disclosed. The transformer includes a closed-magnetic circuit type of core having a gap, a primary winding 7p, a secondary winding 7s and a detecting terminal located on the secondary winding 7s or an additional detecting winding separate from the main winding. The primary winding 7p and secondary winding 7s are wound around a portion apart from a gap 14 of a common core column 13 serving as a center axis. The primary winding 7p is formed of a sheet- or film-like conductor, and the winding portion of the primary winding 7p is arranged so as to include the winding portion of the secondary winding 7s in the direction along the center axis of the core column 13.