Fundamental fixed-point principles. 1.The banach fixed-point theorem and iterative methods. 2.The schauder fixed-point theorem and compactness. Applications of the fundamental fixed-point principles. 3.Ordinary differential equations in B-spaces. 4.Differential calculus and the implicit functions theorem. 5.Newton´s method. 6.Continuation with respect to a parameter. 7.Positive operators. 8.Analytic bifurcation theory. 9.Fixed points of multivalued maps. 10.Nonexpansive operators and iterative methods. 11.Condensing maps and the bourbaki-kneser fixed-point theorem. The mapping degree and the fixed-point index. 12.The Leray-schauder fixed-point index. 13.Applications of the fixed-point index. 14.The fixed-point index of differentiable and analytic maps. 15.Topological bifurcation theory. 16.Essential mapping and the Borsuk antipodal theorem. 17.Asymptotic fixed-point theorems.