Introduction to topology and the Euler characteristic. The first in a series of preparatory lectures for the FREE online Fall 2013 course on topological data analysis offered through the University of Iowa Division of Continuing Education.. For more information see http://www.math.uiowa.edu/~idarcy/AppliedTopology.html Note: The goal of this lecture is to introduce the viewer to topology. Only a partial understanding is needed for the online course. This is an inter-disciplinary course. Thus you only need to have sufficient understanding in order to communicate with others in this course and to follow/participate in the online lectures. A partial understanding of this lecture will suffice. Lecture 2 can be found at https://www.youtube.com/watch?v=2HS9ypIe8es The complete list of preparatory lectures plus additional links can be found at http://homepage.math.uiowa.edu/~idarcy/AT/prelectures.html Some clarifications: p. 3: Example: A blue triangles indicates that the triangle bounds a surface, and thus this example has exactly two faces. The 3 edges bounding a white triangle do not bound a surface (so a white triangle does not correspond to a face). Thus our complex has a "hole". p. 28: Graphs: Identifying Trees When I said that a graph does not contain triangles, I should have said surface or face. As in the middle graph, three edges can form a triangle, but if the complex is a graph, than that triangle cannot bound a face.