The way to the proof of Fermat´s theorem

In the mid-17th Century Pierre de Fermat stated on the margin of a copy of Diophantine´s work the conjecture: there are no natural numbers n⩾3,x,y,z such that xⁿ+yⁿ=zⁿ (Fermat´s last theorem, FLT). In 1993 Andrew Wiles announced the theorem: semi-stable elliptic curves over Q are modular. The present paper explains the meaning of Wiles´ theorem, his strategy to prove it, and why it settles Fermat´s conjecture. We begin by sketching the history of the attempts to prove FLT which reflect its fascination as a challenge for testing the power of the mathematics available