Manifold topology

In this thesis, in the first two chapters, some known facts related to topological spaces are given. In the third chapter, manifold topological?s history and the changes in manifold throughout the years. In the fourth chapter, m-dimensional topological and smooth manifolds are studied. In the last chapter, embeddibility of compact manifolds into an Euclidean space and, in particular, the known classification of 2-dimensional compact manifolds is examined as in Kahn (1995). (Our main references for this study are Bülbül (2004), Kahn (1995) and Sabuncuoğlu (2004).)Key Words: Topological and Smooth Manifold, Compactness, Partitions of Unity, Embedding of Manifolds, Compact Surfaces?