The main result of this chapter is the full statement and proof of the Fundmental Theorem of Galois Theory for finite field extensions in any char-acteristic. The way has been prepared in earlier chapters to make the going smooth here. First, key results are proved on extending field isomorphisms to polynomial rings and also to simple extensions (adjoining one element); familiar examples are presented within ordinary number systems; and a general embedding result is proved for finite field extensions. The problem of constructing field automorphisms of a finite extension of a given ground field is seen to hinge on the existence of roots of a single polynomial; accordingly, the two requirements to finding a full complement of such roots are studied: namely, the presence of a splitting field, and the absence of repeated roots; these ideas lead naturally to the concepts of normal and separable extensions, respectively, which are then studied. Along the way, the derivative of a polynomial and the characteristic of a ring are introduced, and the characteristic zero case is proven to have good properties with respect to separability. The main theorem is stated in three parts, then proved. The chapter concludes with a section of exercises.