Lectures on Real Analysis

I Preliminaries II Metric Spaces and Normed Spaces III Topological Spaces IV Convergence in Topological Spaces V Compactness VI Real Functions on Topological Spaces; Applications VII Three Important Tools of the analyst VIII Topological Vector Spaces IX Linear Transformations X Weak Topologies and Dual Spaces XI Spectral Theory and Compact Operators XII Fixed Point Theorems