Topological ideas are present in almost all areas of today's mathematics. The subject of itself consists of several different branches, such as point set , algebraic and differential , which have relatively little in common. We shall trace the rise of topological concepts in a number of different situations. Perhaps the first work which deserves to be considered as the beginnings of is due to Euler. In 1736 Euler published a paper on the solution of the Königsberg bridge problem entitled Solutio problematis ad geometriam situs pertinentis ....