The first part of the book studies pseudo-periodic maps of a closed surface of genus greater
than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in
1944 as an extension of periodic maps. In this book the conjugacy classes of the (chiral)
pseudo-periodic mapping classes are completely classified and Nielsen's incomplete
classification is corrected. The second part applies the results of the first part to the
topology of degeneration of Riemann surfaces. It is shown that the set of topological types of
all the singular fibers appearing in one parameter holomorphic families of Riemann surfaces is
in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of
negative twists. The correspondence is given by the topological monodromy.
