1 The Banach contraction principle 7.- 2 The Boyd-Wongtheorem 13.- 3 Further extensions of the contraction principle 16.- 4 Weak contractions 23.- 5 Contractions of ε-type 29.- 6 Sequences of maps  and fixed points 36.- 7 Fixed points of non-expansive maps 39.- 8 The Riesz mean ergodic theorem 42.- 9 The Brouwer fixed point theorem 46.- 10 The Schauder-Tychonoff fixed point theorem 50.- 11 Further consequences of the Schauder-Tychonoff theorem 55.- 12 TheMarkov-Kakutani theorem 60.- 13 TheKakutani-Ky Fan theorem 62.- 14 The implicit function theorem 70.- 15 Location of zeros 75.- 16 Ordinary differential equations in Banach spaces 78.- 17 The Lax-Milgram lemma 89.- 18 An abstract elliptic problem 97.- 19 Semilinear evolution equations 101.- 20 An abstract parabolic problem 108.- 21 The invariant subspace problem 114.- 22 Measure preserving maps on compact Hausdorff spaces 118.- 23 Invariant means on semigroups 120.- 24 Haar measures 123.- 25 Game theory 130.- 26 Problems.