Fixed-wing aircraft include monoplanes, biplanes and triplanes; in fact all conventional aircraft that are neither balloons, airships, autogyros, helicopters or tiltrotors are fixed-wing aircraft.
Sir George Cayley, the inventor of the science of aerodynamics, was building and flying models of fixed wing aircraft as early as 1803, and he built a successful passenger-carrying glider in 1853, but it is known the first practical self-powered aeroplanes were designed and constructed by the Wright brothers. (Indeed, the German Karl Jatho had already constructed such 4 months earlier and made his first flight August 28, 1903 in Hanover.) Their first successful test flights were in December 17, 1903 and by 1904 the Flyer III was capable of fully-controllable stable flight for substantial periods. Strictly, its wings were not completely fixed, as it depended for stability on a flexing mechanism named wing warping. This was soon superseded by the competitive development of ailerons, attached to an otherwise rigid wing.
