Preface Metric Spaces: Definition of a Metric Space Some Examples Euclidean Metric in Kn Normed Spaces: Normed Spaces The Sequence Space lp, p>1: Topology of Metric Spaces: Topological Spaces Topology of Metric Spaces Equivalent Metrics Subspaces Sequences in Metric Spaces Closure, Interior and Boundary Complete Metric Spaces: The Cauchy Sequence Subsequences Contraction Mapping Continuity: Continuity between Metric Spaces Open Maps, Closed Maps Uniform Continuity Homeomorphism and Isometry Discontinuities and All That Connected Metric Spaces: Connected Metric Spaces Application of Intermediate Value Theorem Connected Components Path Connected Spaces Compact Metric Spaces: Compactness Characterization of Compact Metric Spaces Applications Sequences and Series of Functions: Pointwise Convergence Uniform Convergence Power Series: Limit Superior and Limit Inferior Power Series The Circular Functions The Exponential Function Fourier Series: Orthogonal Functions Fourier Sine and Cosine Series Mean Square Convergence of Fourier Series The Pointwise Convergence of Fourier Series Appendixes Bibliography Index Index of Symbols.