Errata to the printed and bound version: (note: these errata have already been incorporated in the electronic version) page 10, par 3, line 1: 'For games of perfect information' should be 'For games of imperfect information' page 33, Lemma 4.5.5, line 1: 'then \val^\uparrow(\Gamma(f)) >= v' should be 'then \val^\uparrow(\Gamma(f)) <= v' page 34, proof of Lemma 4.5.5, last line: '.. = u'(e) = v-\epsilon' should be '.. = u'(e) = v+\epsilon' page 38, par 4, line 2: 'hence AD contradicts AC, hence AD contradicts the Axiom of Choice, and has many interesting consequences' should be 'hence AD contradicts the Axiom of Choice. AD has many other interesting consequences'. page 45, par 1, lines 1-2: 'first we, for several different constructions of V from other sets, lemmas constructing strategies in \Gamma^{\omega_1}(V)' should be 'first we give lemmas constructing strategies in \Gamma^{\omega_1}(V), for several different constructions of V from other sets'. page 83, equations (8.41), (8.42) and (8.43): v_0 should be v_{t_0} and v_t should be v_{\tau_r} throughout