Abstract: "Infinite Combinatorial Topology", despite having its roots back in the Cantor era, is a new field in mathematics. This field studies, from a combinatorial point of view, the diagonalization arguments which appear in topological properties and constructions. Many classical properties are put into a general framework, and combinatorial methods are used to obtain new insights into these. We will give a brief, nontechnical survey of (a major aspect of) this active field of research: Its roots, examples of problems and methods used to solve them, and applications. More technical details and examplese are planned to be given in more focused seminars. The field is close enough to the axiomatics so that no prior knowledge is needed, and we believe that exchange of ideas with mathematicians working in other fields will prove useful for this field. As much time as needed will be dedicated for questions and discussions.