  Let A^2 denote the affine plane over an algebraically closed field of
arbitrary characteristic. Besides contributing several new results in the
general theory of birational endomorphisms of A^2, this article describes
certain classes of birational endomorphisms f defined by requiring that the
missing curves or contracting curves of f are lines. The last part of the
article is concerned with the monoid structure of the set of birational
endomorphisms of A^2.
